PHYSICS QUESTION. plz help?

Question

The determined Wile E. Coyote is out once more to try to capture the elusive Road Runner. The coyote wears a new pair of Acme power roller skates, which provide a constant acceleration of 15 m/s^2. The coyote starts off at rest 70 m from the edge of a cliff at the instant the road runner zips by in the direction of the cliff.

a.) If the Road Runner moves constant, find the minimum speed the roadrunner must have in order to reach the cliff before the coyote.

b.) If the cliff is 100 m above the base of a canyon, find where the coyote lands in the canyon. (Assume that his skates are still in operation when he is in flight and that his horizontal component of acceleration remains constant at 15 m/s^2).



thx people

Answer 1

I hate this Road Runner.

Anyway...
The distance for the Coyote Sr must be a bit more than the distance for Sr for the Road Runner.
Sc>=Sr this way the bloody R&R will be just ahead at the end of the 70m.
Sr=Vr tr
Sc=0.5 ac tc^2

so tc=sqrt(2 Sc / ac)

and then Vr=Sr/tr since to come close tr=tc=t and Sc=Sr=S

We have
Vr=S/t=S/ sqrt((2S)/a)
Vr=70 / sqrt((2 x 70)/15)=23 m/s

b)

Vh= V0+at
Vv=gt

Since the poor Coyote will fall 100m his time in flight is
t=sqrt(2h/g)

Now
Vh= V0+a sqrt(2h/g)
Vv=g sqrt(2h/g)
where V0= at= a sqrt((2S)/a)
V0=sqrt((2aS))=sqrt(2 x 15x 70)= 46m/s