Minimum speed?

Question

The determined Wile E. Coyote is out once more to try to capture the elusive roadrunner. The coyote wears a new pair of Acme power roller skates, which provide a constant horizontal acceleration of 10 m/s2. The coyote starts off at rest 60 m from the edge of a cliff at the instant the roadrunner zips by in the direction of the cliff.

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

b. If the cliff is 150 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/s2.)

sorry, constant acceleration is 10 not 15

Answer 1

Is the horizontal acc 10 or 15?
What is the speed of the roadrunner?

I will show the technique and us ah as the coyote's horizontal acceleration.

The roadrunner has
x(t)=v0*t
and the coyote has
x(t)=.5*ah*t^2
the coyote will travel 60 m in time
sqrt(60*2/ah)
therefore the time of the roadrunner must be less
60/v0 or
v0>60/sqrt(60*2/ah)

at the lip of the cliff the coyote has speed
v(lip)=ah*sqrt(60*2/ah)
after the lip, the vertical fall will be
y(t)=150-.5*g*t^2
when y(t)=0, the coyote lands
t=sqrt(150*2/g)
the x(t) past the lip is
x(t)=ah*sqrt(60*2/ah)*t+
.5*ah*t^2

so the landing point is

x(sqrt(150*2/g))=
ah*sqrt(60*2/ah)*
sqrt(150*2/g)+
.5*ah*150*2/g

j

Answer 2

Oh, sorry, you misunderstood. The minimum speed limit on the HIGHWAY in Florida is 40. There is no minimum speed on state roads or residential areas. Generally, 25 is the speed limit in residential areas, 40 is the limit on local roads without residences. Always check road signs to decide which speed to drive. The police will go by whatever the last sign stated on that stretch of road. There is usually a sign right after each major intersection. Good luck and stay out of trouble!! p.s. - if you're behind a senior citizen, you could end up going about 12 m.p.h. Then you just have to chill until you can get around them!