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?

Answer 1

Answer:

Total distance does the grasshopper travel before the cars hit is 150 m

Explanation:

Each car moves x=100 m before they collide. Both the cars moving in constant velocity. time taken t by each car is

$t=\frac{x}{v}$

where x  is the distance traveled with velocity v

$t=\frac{100}{10}\\t=10 sec$

The insect is moving through this time period with a constant velocity of 15 m/s

The distance traveled by grasshopper  is

$distance=V_{gh} \times t\\distance=15 \times 10\\distance=150 m$