A wily coyote ties himself to a rocket capable of an acceleration of 10 m/s^2. T

Question

A wily coyote ties himself to a rocket capable of an acceleration of 10 m/s^2. The coyote and rocket are initially at rest 150 yards to the left of the edge of a cliff. At time t = 0, a roadrunner passes the coyote at a constant speed of 25 mi/hr to the right. At this instant the coyote lights the fuse, which takes an additional 5 seconds to bum down before the rocket can ignite. When the rocket ignites, the roadrunner begins to accelerate at 2 m/s^2. How far does the roadrunner travel between the time he is even with the coyote and the time the fuse ignites the rocket? Can the coyote catch the roadrunner before they reach the end of the cliff?

Explanation / Answer

a)

v = 25 mi/hr = 11.176 m/s

x1 = v*t = 11.176*5 = 55.88 m

b)

d = 150 yards = 137.16 m

for runner

to travel to cliff end

137.16-55.88 = (11.176*t) + (0.5*2*t^2)

time taken = t = 5.02 s

for cayote

x2 = vo*t + 0.5*a*t^2

x2 = 0 + 0.5*10*5.02^2

x2 = 126.002 m < d

the cayote cannot catch the runner

NO

++

c)

i)

for cayote to travel the end of cliff

137.16 = 0.5*10*t^2

t1 = 5.24 s

time elapsed = 5.24-5.02 = 0.22 s

(ii)

distance = 137.16-126.002 = 11.158 m

+++++++++++

d)

cayote velocity = v = a*t = 10*5.02 = 50.2 m/s

runner velocity v= u+a*t = 11.176 + (2*5.02) = 21.216 m/s

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