The problem: Two cars start 250 m apart and drive toward each other at a steady
ID: 1963348 • Letter: T
Question
The problem: Two cars start 250 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 16 m/s relative to the ground. The insect jumps the instant he lands, so he spends no time resting on either car.The sub-question: What total distance does the grasshopper travel before the cars hit?
What i came up with:
I concluded that the cars collide after 12.5 seconds (correct me if i am wrong).
But i just can't understand how i can calculate the distance of the grasshopper because the cars are moving.
Explanation / Answer
to simplify the question, imagine a car just going at 20m/s toward a wall thats 250m away. you said that it takes 12.5sec, 250/20 that's about right. No matter how the car goes, the grasshopper will go 16m per second until there's no more distance to travel (when car stops) 16 * 12.5= 200m 200m traveled.
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