Q7DQ - University Physics with Modern Physics

Question

Sketch the six graphs of the x- and y-components of position, velocity, and acceleration versus time for projectile motion with ${\mathit{x}}_{\mathbf{0}}\mathbf{=}{\mathit{y}}_{\mathbf{0}}\mathbf{=}\mathbf{0}\mathbf{ }$and $\mathbf{0}\mathbf{<}{\mathit{\alpha }}_{\mathbf{0}}\mathbf{<}\mathbf{90}\mathbf{°}$.

Step-by-Step Solution

Answer

The diagram for position, velocity, acceleration versus time is

                                 

Step 1: Concept/Significance of projectile.

A projectile is an object that follows a parabolic route when it is projected with velocity not directly upwards but at an angle to the horizontal.

Step 3: sketch of position, velocity, and acceleration versus time for projectile motion.

Consider the x axis. The initial horizontal component of the velocity remains constant during the flight in the absence of air resistance, i.e.,

$v_x=\mathrm{constant}$.

It follows from this that the horizontal distance travelled increases linearly with time. The horizontal acceleration is also 0 since there is no force in the direction.

Let's have a look at the next step, which is a little more complicated. For starters, we now have an acceleration of $a=-g$.

The y coordinate follows a parabolic trajectory, as it does for any projectile motion. Finally, as the flight progresses, the speed drops - initially positive, then negative.

Thus, graph for position, velocity, acceleration versus time is