# 2d motion question

oreosama

## Homework Statement

wiley e coyote is out once more to try to capture the elusive roadrunner. the coyote wears a pair of acme jet powered roller skates, which provide a constant horizontal acceleration ac. the coyote starts off at rest D meters from the edge of a cliff at the instant the roadrunner zips by in the direction of the cliff. the cliff is H meters above the canyon floor. given [ac, D, H], determine:

if the roadrunner moves at constant speed, what should the roadrunners min speed be in order to reach the cliff before the coyote?

as usual the roadrunner is saved by making a sudden turn at the cliff. determine where the coyote lands in the canyon. (assume skates still on)

the velocity of the coyote just before hitting the canyon floor

## Homework Equations

vx=v0x+at
x=x0+v0x*t+1/2*a*t^2
vx^2=v0x^2 + 2a(x - x0)

and y equivilents

## The Attempt at a Solution

for a, i solved for time(t1) as t1= sqrt(2D/ac), which i then use for velocity of roadrunner(Vr) as Vr= D/sqrt(2D/ac)

for b & c, i used info from solving things in a as info to parameters:

from D to bottom of cliff

x0= D
x= D2
Vx0= acsqrt(2D/ac)
Vx= ?
a = ac

y0=0
y= H
Vy0 = 0
Vy = ?
a = g

t=t2

trying to use my y-based equations to solve for t2 results in them collapsing

Vy= 0 + gt2
Vy^2 = 0^2 + 2gH

g^2*(t2)^2 = 2gH

H = (g*t2^2)/2

(g*t2^2)/2 = 0 + 0 + 1/2*g*(t2)^2

everything cancels :<