Q64P - University Physics with Modern Physics

Question

Two cars start 200 m apart and drive toward each other at a steady 10 m/s. On the front of one of them, an energetic grasshopper jumps back and forth between the cars (he has strong legs!) with a constant horizontal velocity of 15 m/s relative to the ground. The insect jumps the instant he lands, so he spends no time resting on either car. What total distance does the grasshopper travel before the cars hit?

Step-by-Step Solution

Answer

the distance the grasshopper travelled before getting hit by the car is 150 m.

Step 1: Identification of the given data

The given data can be expressed below as:

• The distance between the cars is 200 m.
• The velocity of the cars is 10 m/s.
• The velocity of the grasshopper is 15 m/s.

Step 2: Significance of the Newton’s first law for finding the distance

This law states that a particular object will continue to move in a constant velocity or uniform velocity if it is not being resisted by an external object.

The equation of displacement gives the time required for the grasshopper to travel and the equation of displacement gives the distance travelled by the grasshopper.

Step 3: Determination of the total distance of the grasshopper

From Newton’s first law, the equation of displacement of the car is expressed as:

 = vt

Here, s is the distance travelled by each of the car that is 100 m as both the cars start from 200 m apart and v is the constant velocity of the car that is 10 m/s.

Substituting the values in the above equation, we get-

$$\begin{gathered} 100 m=\left(10 m/s\right)\times t \\ t=10 s \end{gathered}$$

Hence, the equation of distance for the grasshopper is expressed as:

s = vt

Here, s is the distance travelled by the grasshopper, v is the velocity of the grasshopper that is 15 m/s and t is the time taken by the grasshopper that is 10 s.

Substituting the values in the above equations, we get-

$\begin{array}{l}s=15 m/s\times 10s\\ =150 m\end{array}$

Thus, the distance the grasshopper travelled before getting hit by the car is 150 m.