Wile E has constant horizontal acceleration of 15 m/s sqrd Starts from rest 70 m from edge of cliff.?

Question

if coyote starts off at rest 70 m from edge of cliff the instant roadrunner zips by in direction of cliff and moves with constant speed find the minimum speed roadrunner has to reach cliff before coyote.

The answer is 23 m/s sqrd. I have not been able to get this answer

Answer 1

Wile E Coyote starts from rest (u=0), accelerating at a constant rate (a = 15 m/s^2), and covers a distance s=70m. We need to find his velocity at the cliff edge.

v^2 = u^2 + 2as = 2as (as u=0)

v^2 = 2*15*70 = 2100

v = 45.8 m/s

Thus Roadrunner must be moving at least equal to or faster than this.

EDIT: I'm partially wrong here in my logic. We need to find how long it takes the coyote to reach the cliff edge.

s = u*t + (1/2)*a*t^2 = (1/2)*a*t^2 (as u = 0)

t^2 = 2*s/a = 2*70/15 = 9.33 s^2

t = 3.1 s

This is the fastest time in which coyote can reach the cliff edge. Therefore roadrunner must cover that distance in at least the same time or faster.

To cover a distance of 70 m in 3.1 s means that roadrunner must be moving at 70/3.1 = 22.6 m/s at a minimum.

Answer 2

It hardly matters. The roadrunner will be able to stop successfully just at the edge of the cliff, while the coyote will go over the side, regardless of relative speeds.

Answer 3

Dudara is on the right path but since the Coyote is accelerating we need to figure out the amount of time it takes the Coyote to reach the edge. Then we can figure out how fast roadrunner needs to travel in order to reach the edge in less time.. roughly 3 secs. ??