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 prestunt 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

speed at the start of ramp, u = 10.4 m/s

perpendicular to the ramp,

N - mgcos20 = 0

N = mgcos20

friction force, f = uN = umg = 0.02mgcos20

along the ramp,

Fnet = mgsin20 + 0.02mgcos20

a = Fnet / m = (gsin20 + 0.02gcos20) = 3.54 m/s^2

distance along the ramp, d = h/sin20 = 2/sin20 = 5.85 m

using v^2 - u^2 = 2ad

v^2 - 10.4^2 =2(-3.54)(5.85)

v= 8.17 m/s

so bike will launch with speed 8.17 m/s at an angle of 20 deg .

In vertical :

vy = 8.17sin20 = 2.79 m/s

ay = - 9.8 m/s^2

y = -2 m

using d = ut + at^2 /2

-2 = 2.79t - 4.9t^2

4.9t^2 - 2.79t - 2 = 0

t = 0.984 s

horizontal distance traveled = vcos20 * t

       = 8.17cos20 x 0.984

= 7.55 m

this is less than 10 m

so he will be crocodile food.

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