You are watching one of the Red Bull extreme sport competitions on tv, where a s

Question

You are watching one of the Red Bull extreme sport competitions on tv, where a stunt person planes to ride their motorcycle up a 2.0 m high, 20 degree ramp, sail across a 10 m wide pool filled with hungry crocodiles, and land at ground level on the other side. During the prestart interview, the stunt person brags about all of the practice runs where things went super well. Unfortunately during the televised stunt, the motorcycle engine dies just as they start up the ramp. The motorcycle is going 10.4 m/s at that instant, and the rolling friction of the rubber tires (coefficient 0.02) is not negligible. Does the stunt person survive, or are they crocodile food? Justify your answer by calculating the distance they travel through the air after leaving the end of the ramp.

Explanation / Answer

let us 1st find the velocity at the top of incline
use:
kinetic energy at bottom = potential energy at top + kinetic energy at top + energy lost against friction
0.5*m*vi^2 = m*g*h +0.5*m*v^2 + miu*m*g*cos thetha*d
0.5*m*vi^2 = m*g*h +0.5*m*v^2 + miu*m*g*cos thetha*(h/sin thetha)
0.5*m*vi^2 = m*g*h +0.5*m*v^2 + miu*m*g*cot thetha*h
0.5*vi^2 = g*h +0.5*v^2 + miu*g*cot thetha*h
0.5*10.4^2 = 9.8*2 + 0.5*v^2 + 0.02 * 9.8*cot 20 * 2
54.08 = 19.6 + 0.5*v^2 + 1.08
v = 8.17 m/s

Now consider the projectile motion from top:
for vertical motion:
vi = v*sin 20 = 8.17*sin 20 = 2.79 m/s
d = - 2m
a = -9.8 m/s^2
d = vi*t + 0.5*a*t^2
-2 = 2.79*t + 0.5*(-9.8)*t^2
4.9*t^2 - 2.79*t - 2 = 0

SOlving above quadratic equation,
positive value of t = 0.984 s

For horizontal motion:
vi = v*cos 20 = 8.17*cos 20 = 7.68 m/s
t= 0.984 s
Horizontal distance = vi*t
= 7.68*0.984
= 7.55 m

But width is 10 m
He will not be able to cross

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