Chapter 8

(a) What is the magnitude of the momentum of a \(10,000-\mathrm{kg}\) truck whose speed is 12.0 \(\mathrm{m} / \mathrm{s} ?\) (b) What speed would a \(2000-\mathrm{kg}\) SUV have to attain in order to have (i) the same momentum? (ii) the same kinetic energy?

In a certain men's track and field event, the shotput has a mass of 7.30 \(\mathrm{kg}\) and is released with a speed of 15.0 \(\mathrm{m} / \mathrm{s}\) at \(40.0^{\circ}\) above the horizontal over a man's straight left leg. What are the initial horizontal and vertical components of the momentum of this shotput?

( a) Show that the kinetic energy \(K\) and the momentum magnitude \(p\) of a particle with mass \(m\) are related by \(K=p^{2} / 2 m\) (b) \(A 0.040\) -kg cardinal (Richmondena cardinalis) and a 0.145 -kg baseball have the same kinetic energy. Which has the greater magnitude of momentum? What is the ratio of the cardinal's magnitude of momentum to the baseball's? (c) A \(700-\mathrm{N}\) man and a \(450-\mathrm{N}\) woman have the same momentum. Who has the greater kinetic energy? What is the ratio of the man's kinetic energy to that of the woman?

Two vehicles are approaching an intersection. One is a \(2500-\mathrm{kg}\) traveling at 14.0 \(\mathrm{m} / \mathrm{s}\) from east to west (the \(-x\) -direction), and the other is a 1500 -kg sedan going from south to north (the \(+y\) -direction) at 23.0 \(\mathrm{m} / \mathrm{s}\) . (a) Find the \(x\) - and \(y\) -components of the net momentum of this system. (b) What are the magnitude and direction of the net momentum?

One 110 -kg football lineman is running to the right at 2.75 \(\mathrm{m} / \mathrm{s}\) while another 125 -kg lineman is running directly toward him at 2.60 \(\mathrm{m} / \mathrm{s}\) . What are (a) the magnitude and direction of the net momentum of these two athletes, and (b) their total kinetic energy?

BIO Biomechanics. The mass of a regulation tennis ball is 57 g (although it can vary slightly), and tests have shown that the ball is in contact with the tennis racket for 30 \(\mathrm{ms}\) . (This number can also vary, depending on the racket and swing.) We shall assume a 30.0 -ms contact time for this exercise. The fastest-known served tennis ball was served by "Big Bill" Tilden in \(1931,\) and its speed was measured to be 73.14 \(\mathrm{m} / \mathrm{s}\) . (a) What impulse and what force did Big Bill exert on the tennis ball in his record serve? (b) If Big Bill's opponent returned his serve with a speed of \(55 \mathrm{m} / \mathrm{s},\) what force and what impulse did he exert on the ball, assuming only horizontal motion?

Force of a Golf Swing. \(A 0.0450-\mathrm{kg}\) golf ball initially at rest is given a speed of 25.0 \(\mathrm{m} / \mathrm{s}\) when a club strikes. If the club and ball are in contact for \(2.00 \mathrm{ms},\) what average force acts on the ball? Is the effect of the ball's weight during the time of contact significant? Why or why not?

Force of a Baseball Swing. A baseball has mass 0.145 \(\mathrm{kg}\) . (a) If the velocity of a pitched ball has a magnitude of 45.0 \(\mathrm{m} / \mathrm{s}\) and the batted ball's velocity is 55.0 \(\mathrm{m} / \mathrm{s}\) in the opposite direction, find the magnitude of the change in momentum of the ball and of the impulse applied to it by the bat. (b) If the ball remains in contact with the bat for 2.00 \(\mathrm{ms}\) , find the magnitude of the average force applied by the bat.

A 0.160 -kg hockey puck is moving on an icy, frictionless, horizontal surface. At \(t=0,\) the puck is moving to the right at 3.00 \(\mathrm{m} / \mathrm{s} .\) (a) Calculate the velocity of the puck (magnitude and direction) after a force of 25.0 \(\mathrm{N}\) directed to the right has been applied for 0.050 s. (b) If, instead, a force of 12.0 \(\mathrm{N}\) directed to the left is applied from \(t=0\) to \(t=0.050 \mathrm{s}\) , what is the final velocity of the puck?

An engine of the orbital maneuvering system (OMS) on a space shuttle exerts a force of \((26,700 \mathrm{N}) \hat{J}\) for 3.90 \(\mathrm{s}\) , exhausting a negligible mass of fuel relative to the \(95,000-\mathrm{kg}\) mass of the shuttle. (a) What is the impulse of the force for this 3.90 s? (b) What is the shuttle's change in momentum from this impulse? (c) What is the shuttle's change in velocity from this impulse? (d) Why can't we find the resulting change in the kinetic energy of the shuttle?

CALC At time \(t=0,\) a 2150 -kg rocket in outer space fires an engine that exerts an increasing force on it in the \(+x\) -direction. This force obeys the equation \(F_{x}=A t^{2},\) where \(t\) is time, and has a magnitude of 781.25 \(\mathrm{N}\) when \(t=1.25 \mathrm{s}\) . (a) Find the SI value of the constant \(A,\) including its units. (b) What impulse does the engine exert on the rocket during the 1.50 -s interval starting 2.00 \(\mathrm{s}\) after the engine is fired? (c) By how much does the rocket's velocity change during this interval?

A bat strikes a 0.145 -kg baseball. Just before impact, the ball is traveling horizontally to the right at \(50.0 \mathrm{m} / \mathrm{s},\) and it leaves the bat traveling to the left at an angle of \(30^{\circ}\) above horizontal with a speed of 65.0 \(\mathrm{m} / \mathrm{s}\) . If the ball and bat are in contact for 1.75 \(\mathrm{ms}\) find the horizontal and vertical components of the average force on the ball.

To warm up for a match, a tennis player hits the \(57.0-\) g ball vertically with her racket. If the ball is stationary just before it is hit and goes 5.50 \(\mathrm{m}\) high, what impulse did she impart to it?

CALC Starting at \(t=0,\) a horizontal net force \(\vec{F}=\) \((0.280 \mathrm{N} / \mathrm{s}) \hat{t} \hat{\imath}+\left(-0.450 \mathrm{N} / \mathrm{s}^{2}\right) t^{2} \hat{\mathrm{J}}\) is applied to a box that has an initial momentum \(\vec{p}=(-3.00 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}) \hat{\imath}+(4.00 \mathrm{kg} \cdot \) \(\mathrm{m} / \mathrm{s} ) \hat{\boldsymbol{J}}\) . What is the momentum of the box at \(t=2.00 \mathrm{s} ?\)

The expanding gases that leave the muzzle of a rifle also contribute to the recoil. A 30 -caliber bullet has mass 0.00720 \(\mathrm{kg}\) and a speed of 601 \(\mathrm{m} / \mathrm{s}\) relative to the muzzle when fired from a rifle that has mass 2.80 \(\mathrm{kg}\) . The loosely held rifle recoils at a speed of 1.85 \(\mathrm{m} / \mathrm{s}\) relative to the earth. Find the momentum of the propellant gases in a coordinate system attached to the earth as they leave the muzzle of the rifle.

A \(68.5-k g\) astronaut is doing a repair in space on the orbit ing space station. She throws a 2.25 -kg tool away from her at 3.20 \(\mathrm{m} / \mathrm{s}\) relative to the space station. With what speed and in what direction will she begin to move?

Animal Propulsion. Squids and octopuses propel themselves by expelling water. They do this by keeping water in a cavity and then suddenly contracting the cavity to force out the water through an opening. A \(6.50-\) kg squid (including the water in the cavity) at rest suddenly sees a dangerous predator. (a) If the squid has 1.75 \(\mathrm{kg}\) of water in its cavity, at what speed must it expel this water to suddenly achieve a speed of 2.50 \(\mathrm{m} / \mathrm{s}\) to escape the predator? Neglect any drag effects of the surrounding water. (b) How much kinetic energy does the squid create by this maneuver?

You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a 0.400 -kg ball that is traveling horizontally at 10.0 \(\mathrm{m} / \mathrm{s}\) . Your mass is 70.0 \(\mathrm{kg}\) . (a) If you catch the ball, with what speed do you and the ball move afterward? (b) If the ball hits you and bounces off your chest, so afterward it is moving horizontally at 8.0 \(\mathrm{m} / \mathrm{s}\) in the opposite direction, what is your speed after the collision?

On a frictionless, horizontal air table, puck \(A\) (with mass 0.250 \(\mathrm{kg}\) is moving toward puck \(B\) (with mass \(0.350 \mathrm{kg} ),\) which is initially at rest. After the collision, puck \(A\) has a velocity of 0.120 \(\mathrm{m} / \mathrm{s}\) to the left, and puck \(B\) has a velocity of 0.650 \(\mathrm{m} / \mathrm{s}\) to the right. (a) What was the speed of puck \(A\) before the collision? (b) Calculate the change in the total kinetic energy of the system that occurs during the collision.

When cars are equipped with flexible bumpers, they will bounce off each other during low-speed collisions, thus causing less damage. In one such accident, a 1750 -kg car traveling to the right at 1.50 \(\mathrm{m} / \mathrm{s}\) collides with a \(1450-\mathrm{kg}\) car going to the left at 1.10 \(\mathrm{m} / \mathrm{s} .\) Measurements show that the heavier car's speed just after the collision was 0.250 \(\mathrm{m} / \mathrm{s}\) in its original direction. You can ignore any road friction during the collision. (a) What was the speed of the lighter car just after the collision? (b) Calculate the change in the combined kinetic energy of the two-car system during this collision.

Two identical 1.50-kg masses are pressed against opposite ends of a light spring of force constant \(1.75 \mathrm{N} / \mathrm{cm},\) compressing the spring by 20.0 \(\mathrm{cm}\) from its normal length. Find the speed of each mass when it has moved free of the spring on a frictionless horizontal table.

Block \(A\) in Fig. E8.24 has mass \(1.00 \mathrm{kg},\) and block \(B\) has mass 3.00 \(\mathrm{kg}\) . The blocks are forced together, compressing a spring \(S\) between them; then the system is released from rest on a level, frictionless surface. The spring, which has negligible mass, is not fastened to either block and drops to the surface after it has expanded. Block \(B\) acquires a speed of 1.20 \(\mathrm{m} / \mathrm{s}\) . (a) What is the final speed of block \(A\) ? (b) How much potential energy was stored in the compressed spring?

A hunter on a frozen, essentially frictionless pond uses a rifle that shoots 4.20 -g bullets at 965 \(\mathrm{m} / \mathrm{s}\) . The mass of the hunter (including his gun) is \(72.5 \mathrm{kg},\) and the hunter holds tight to the gun after firing it. Find the recoil velocity of the hunter if he fires the rifle (a) horizontally and (b) at \(56.0^{\circ}\) above the horizontal.

An atomic nucleus suddenly bursts apart (fissions) into two pieces. Piece \(A,\) of mass \(m_{A},\) travels off to the left with speed \(v_{A} .\) Piece \(B,\) of mass \(m_{B},\) travels off to the right with speed \(v_{B}\). (a) Use conservation of momentum to solve for \(v_{B}\) in terms of \(m_{A}\) , \(m_{B},\) and \(v_{A}\) . (b) Use the results of part (a) to show that \(K_{A} / K_{B}=m_{B} / m_{A},\) where \(K_{A}\) and \(K_{B}\) are the kinetic energies of the two pieces.

Two ice skaters, Daniel (mass 65.0 \(\mathrm{kg} )\) and Rebecca (mass \(45.0 \mathrm{kg} ),\) are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 13.0 \(\mathrm{m} / \mathrm{s}\) before she collides with him. After the collision, Rebecca has a velocity of magnitude 8.00 \(\mathrm{m} / \mathrm{s}\) at an angle of \(53.1^{\circ}\) from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink. (a) What are the magnitude and direction of Daniel's velocity after the collision? (b) What is the change in total kinetic energy of the two skaters as a result of the collision?

You are standing on a large sheet of frictionless ice and holding a large rock. In order to get off the ice, you throw the rock so it has velocity 12.0 \(\mathrm{m} / \mathrm{s}\) relative to the earth at an angle of \(35.0^{\circ}\) above the horizontal. If your mass is 70.0 \(\mathrm{kg}\) and the rock's mass is \(15.0 \mathrm{kg},\) what is your speed after you throw the rock? (See Discussion Question \(\mathrm{Q} 8.7 . )\)

Changing Mass. An open-topped freight car with mass \(24,000 \mathrm{kg}\) is coasting without friction along a level track. It is raining very hard, and the rain is falling vertically downward. Originally, the car is empty and moving with a speed of 4.00 \(\mathrm{m} / \mathrm{s}\).(a) What is the speed of the car after it has collected 3000 \(\mathrm{kg}\) of rain- water? (b) since the rain is falling downward, how is it able to affect the horizontal motion of the car?

An astronaut in space cannot use a conventional means, such as a scale or balance, to determine the mass of an object. But she does have devices to measure distance and time accurately. She knows her own mass is 78.4 \(\mathrm{kg}\) , but she is unsure of the mass of a large gas canister in the airless rocket. When this canister is approaching her at 3.50 \(\mathrm{m} / \mathrm{s}\) , she pushes against it, which slows it down to 1.20 \(\mathrm{m} / \mathrm{s}\) (but does not reverse it) and gives her a speed of 2.40 \(\mathrm{m} / \mathrm{s} .\) What is the mass of this canister?

Two skaters collide and grab on to each other on frictionless ice. One of them, of mass \(70.0 \mathrm{kg},\) is moving to the right at \(2.00 \mathrm{m} / \mathrm{s},\) while the other, of mass \(65.0 \mathrm{kg},\) is moving to the left at 2.50 m/s. What are the magnitude and direction of the velocity of these skaters just after they collide?

A 15.0 -kg fish swimming at 1.10 \(\mathrm{m} / \mathrm{s}\) suddenly gobbles up a 4.50 -kg fish that is initially stationary. Neglect any drag effects of the water. (a) Find the speed of the large fish just after it eats the small one. (b) How much mechanical energy was dissipated during this meal?

Two fun-loving otters are sliding toward each other on a muddy (and hence frictionless) horizontal surface. One of them, of mass \(7.50 \mathrm{kg},\) is sliding to the left at \(5.00 \mathrm{m} / \mathrm{s},\) while the other, of mass \(5.75 \mathrm{kg},\) is slipping to the right at 6.00 \(\mathrm{m} / \mathrm{s} .\) They hold fast to each other after they collide. (a) Find the magnitude and direction of the velocity of these free-spirited otters right after they collide. (b) How much mechanical energy dissipates during this play?

Deep Impact Mission. In July \(2005,\) NASA's "Deep Impact" mission crashed a 372 -kg probe directly onto the surface of the comet Tempel 1 , hitting the surface at \(37,000 \mathrm{km} / \mathrm{h}\) . The original speed of the comet at that time was about \(40,000 \mathrm{km} / \mathrm{h}\) , and its mass was estimated to be in the range \((0.10-2.5) \times\) \(10^{14} \mathrm{kg} .\) Use the smallest value of the estimated mass. (a) What change in the comet's velocity did this collision produce? Would this change be noticeable? (b) Suppose this comet were to hit the earth and fuse with it. By how much would it change our planet's velocity? Would this change be noticeable? (The mass of the earth is \(5.97 \times 10^{24} \mathrm{kg} .\) )

A \(1050\) -kg sports car is moving westbound at 15.0 \(\mathrm{m} / \mathrm{s}\) on a level road when it collides with a 6320 -kg truck driving east on the same road at 10.0 \(\mathrm{m} / \mathrm{s}\) . The two vehicles remain locked together after the collision. (a) What is the velocity (magnitude and direction) of the two vehicles just after the collision? (b) At what speed should the truck have been moving so that it and the car are both stopped in the collision? (c) Find the change in kinetic energy of the system of two vehicles for the situations of part (a) and part (b). For which situation is the change in kinetic energy greater in magnitude?

On a very muddy football field, a 110 -kg linebacker tackles an \(85-\) kg halfback. Immediately before the collision, the line-backer is slipping with a velocity of 8.8 \(\mathrm{m} / \mathrm{s}\) north and the halfback is sliding with a velocity of 7.2 \(\mathrm{m} / \mathrm{s}\) east. What is the velocity (magnitude and direction) at which the two players move together immediately after the collision?

Accident Analysis. Two cars collide at an intersection. Car \(A,\) with a mass of 2000 \(\mathrm{kg}\) , is going from west to east, while car \(B,\) of mass \(1500 \mathrm{kg},\) is going from north to south at 15 \(\mathrm{m} / \mathrm{s}\) . As a result of this collision, the two cars become enmeshed and move as one afterward. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of \(65^{\circ}\) south of east from the point of impact. (a) How fast were the enmeshed cars moving just after the collision? (b) How fast was car \(A\) going just before the collision?

Two cars, one a compact with mass 1200 \(\mathrm{kg}\) and the other a large gas-guzzler with mass \(3000 \mathrm{kg},\) collide head-on at typical freeway speeds. (a) Which car has a greater magnitude of momentum change? Which car has a greater velocity change? (b) If the larger car changes its velocity by \(\Delta v\) , calculate the change in the velocity of the small car in terms of \(\Delta v .\) (c) Which car's occupants would you expect to sustain greater injuries? Explain.

Bird Defense. To protect their young in the nest, falcons will fly into birds of prey (such as ravens) at high speed. In one such episode, a \(600-\) g falcon flying at 20.0 \(\mathrm{m} / \mathrm{s}\) hit a 1.50 -kg raven flying at 9.0 \(\mathrm{m} / \mathrm{s} .\) The falcon hit the raven at right angles to its original path and bounced back at 5.0 \(\mathrm{m} / \mathrm{s}\) . (These figures were estimated by the author as he watched this attack occur in northern New Mexico.) (a) By what angle did the falcon change the raven's direction of motion? (b) What was the raven's speed right after the collision?

A 5.00 -g bullet is fired horizontally into a 1.20 -kg wooden block resting on a horizontal surface. The coefficient of kinetic friction between block and surface is \(0.20 .\) The bullet remains embedded in the block, which is observed to slide 0.230 \(\mathrm{m}\) along the surface before stopping. What was the initial speed of the bullet?

A Ballistic Pendulum. A 12.0 - rifle bullet is fired with a speed of 380 \(\mathrm{m} / \mathrm{s}\) into a ballistic pendulum with mass 6.00 \(\mathrm{kg}\) , suspended from a cord 70.0 \(\mathrm{cm}\) long (see Example 8.8 in Section 8.3). Compute (a) the vertical height through which the pendulum rises, (b) the initial kinetic energy of the bullet, and (c) the kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the pendulum.

Combining Conservation Laws. A 15.0 -kg block is attached to a very light horizontal spring of force constant 500.0 \(\mathrm{N} / \mathrm{m}\) and is resting on a frictionless horizontal table. (Fig. E8.44). Suddenly it is struck by a 3.00 -kg stone traveling horizontally at 8.00 \(\mathrm{m} / \mathrm{s}\) to the right, whereupon the stone rebounds at 2.00 \(\mathrm{m} / \mathrm{s}\) horizontally to the left. Find the maximum distance that the block will compress the spring after the collision.

A \(0.150-\mathrm{kg}\) glider is moving to the right on a frictionless, horizontal air track with a speed of 0.80 \(\mathrm{m} / \mathrm{s} .\) It has a head-on collision with a 0.300 -kg glider that is moving to the left with a speed of 2.20 \(\mathrm{m} / \mathrm{s} .\) Find the final velocity (magnitude and direction) of each glider if the collision is elastic.

A 10.0 -g marble slides to the left with a velocity of magnitude 0.400 \(\mathrm{m} / \mathrm{s}\) on the frictionless, horizontal surface of an icy New York side- walk and has a head- on, elastic collision with a larger 30.0 -g marble sliding to the right with a velocity of magnitude 0.200 \(\mathrm{m} / \mathrm{s}(\mathrm{Fig} . \mathrm{E} 8.48) .\) (a) Find the velocity of each marble (magnitude and direction) after the collision. (Since the collision is head-on, all the motion is along a line.) (b) Calculate the change in momentum (that is, the momentum after the collision minus the momentum before the collision for each marble. Compare the values you get for each marble. (c) Calculate the change in kinetic energy (that is, the kinetic energy after the collision minus the kinetic energy before the collision) for each marble. Compare the values you get for each marble.

You are at the controls of a particle accelerator, sending a beam of \(1.50 \times 10^{7} \mathrm{m} / \mathrm{s}\) protons (mass \(m )\) at a gas target of an unknown element. Your detector tells you that some protons bounce straight back after a collision with one of the nuclei of the unknown element. All such protons rebound with a speed of \(1.20 \times 10^{7} \mathrm{m} / \mathrm{s}\) . Assume that the initial speed of the target nucleus is negligible and the collision is elastic. (a) Find the mass of one nucleus of the unknown element. Express your answer in terms of the proton mass \(m .\) (b) What is the speed of the unknown nucleus immediately after such a collision?

Three odd-shaped blocks of chocolate have the following masses and center-of- mass coordinates: \((1) 0.300 \mathrm{kg},(0.200 \mathrm{m},\) \(0.300 \mathrm{m} ) ;\) (2) \(0.400 \mathrm{kg},(0.100 \mathrm{m},-0.400 \mathrm{m}) ;\) (3) 0.200 \(\mathrm{kg}\) \((-0.300 \mathrm{m}, 0.600 \mathrm{m}) .\) Find the coordinates of the center of mass of the system of three chocolate blocks.

Pluto and Charon. Pluto's diameter is approximately \(2370 \mathrm{km},\) and the diameter of its satellite Charon is 1250 \(\mathrm{km}\) . Although the distance varies, they are often about \(19,700 \mathrm{km}\) apart, center to center. Assuming that both Pluto and Charon have the same composition and hence the same average density, find the location of the center of mass of this system relative to the center of Pluto.

A 1200 -kg station wagon is moving along a straight highway at 12.0 \(\mathrm{m} / \mathrm{s}\) . Another car, with mass 1800 \(\mathrm{kg}\) and speed \(20.0 \mathrm{m} / \mathrm{s},\) has its center of mass 40.0 \(\mathrm{m}\) ahead of the center of mass of the station wagon (Fig. E8.54). (a) Find the position of the center of mass of the system consisting of the two automobiles. (b) Find the magnitude of the total momentum of the system from the given data. (c) Find the speed of the center of mass of the system. (d) Find the total momentum of the system, using the speed of the center of mass. Compare your result with that of part (b).

A machine part consists of a thin, uniform \(4.00-\mathrm{kg}\) bar that is 1.50 \(\mathrm{m}\) long, hinged perpendicular to a similar vertical bar of mass 3.00 \(\mathrm{kg}\) and length 1.80 \(\mathrm{m} .\) The longer bar has a small but dense \(2.00-\mathrm{kg}\) ball at one end (Fig. E8.55). By what distance will the center of mass of this part move horizontally and vertically if the vertical bar is pivoted counterclockwise through \(90^{\circ}\) to make the entire part horizontal?

At one instant, the center of mass of a system of two particles is located on the \(x\) -axis at \(x=2.0 \mathrm{m}\) and has a velocity of \((5.0 \mathrm{m} / \mathrm{s}) \hat{\imath} .\) One of the particles is at the origin. The other particle has a mass of 0.10 \(\mathrm{kg}\) and is at rest on the \(x\) -axis at \(x=8.0 \mathrm{m}\) . (a) What is the mass of the particle at the origin? (b) Calculate the total momentum of this system. (c) What is the velocity of the particle at the origin?

CALC A system consists of two particles. At \(t=0\) one particle is at the origin; the other, which has a mass of \(0.50 \mathrm{kg},\) is on the \(y\) -axis at \(y=6.0 \mathrm{m} .\) At \(t=0\) the center of mass of the system is on the \(y\) -axis at \(y=2.4 \mathrm{m} .\) The velocity of the center of mass is given by \(\left(0.75 \mathrm{m} / \mathrm{s}^{3}\right) t^{2} \hat{\imath}\) (a) Find the total mass of the system. (b) Find the acceleration of the center of mass at any time \(t .\) (c) Find the net external force acting on the system at \(t=3.0 \mathrm{s}\) .

CALC A radio-controlled model airplane has a momentum given by \(\left[\left(-0.75 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}^{3}\right) t^{2}+(3.0 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s})\right] \hat{\imath}+(0.25 \mathrm{kg} \cdot \) \(\mathrm{m} / \mathrm{s}^{2} ) t \hat{J} .\) What are the \(x-, y-\) and \(z\) -components of the net force on the airplane?