Once again the determined coyote is out to get the roadrunner. He has a new pair

Question

Once again the determined coyote is out to get the roadrunner. He has a new pair of power skates that provide a constant acceleration of 6.0 m/s² along the flat top of the mesa. He starts off from rest 48.0 m from the edge of a cliff just as the roadrunner zips past, toward the cliff at constant speed.

a) Calculate how long it takes the coyote to reach the edge of the cliff.
V= V0 + at
24.0 m/s= 0 + (6.0 m/s²)t
t= 4.0sec

b) What is his speed just as he gets there?
V²= V0² + 2as
V²= 0 + 2(6.0 m/s²)(48.0m)
V²= 576 m²/s²
V= v576 m/s
V= 24.0 m/s

c) Calculate the minimum constant speed of the roadrunner in order to escape the clutches of the coyote.
Min Speed = 48.0 m/ 4.0 s = 12.0 m/s

d) Calculate how far from the cliff’s edge the coyote lands in the canyon 78.4 m below. His power skates do not provide acceleration when he is air-borne.
Y= y0 + Vy0(t) + (1/2)ay(t)²
Y= y0 + Vy0(t) – (1/2)g(t)²
0= 78.4 m + 0 – (1/2)(9.8 m/s²)t²
0= 78.4 + 0 – 4.9t²
4.9t²= 78.4
t²= 16
t= v16
t= 4.0sec

x= x0 + vx0(t) + (1/2)ax(t)²
x= 0 +(24.0 m/s)(4.0s)+(1/2)(6.0 m/s²)(4.0s)²
x= 144 m







e) What is his velocity on the cactus laden canyon base when he lands there?
Vx= Vx0 + ax(t)
Vx= (24.0 m/s) + (6.0 m/s²)(4.0s)
Vx= 48.0 m/s

Vy= Vy0 + ay(t)
Vy= Vy0 – g(t)
Vy= 0 – (9.8 m/s²)(4.0s)
Vy= -39.2 m/s

V=(vx² +vy²)^1/2 = (48)² + (39.2)²)^1/2 = 61.972 m/s

Explanation / Answer

distance = ut+0.5at2

u=0, a= 6m/s2, ditance = 48m

therefore time = 4 seconds

speed = u + at = 0 + 6*4= 24 m/s

minimum speed = um

then um *4s= 48m which gives um=12m/s

height is 78.4m, acceleration due to gravity is 9.8m/s2 then

time too reach bottom = [height/(.5g)].5 which gives time = 4s

distance travelled = 24 * 4+0.5*0*16= 96m [His power skates do not provide acceleration when he is air-borne. therefore acceleration is zero].

vertical velocity acheived vv= 9.8*4= 39.2 m/s

horizontal velocity vh= 24m/s

therefore total velocity magnitude = [vv2+vh2].5 = 45.963m/s

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