A motorcycle daredevil plans to ride up a 2.1 m high 23.5 degree ramp, sail acro

Question

A motorcycle daredevil plans to ride up a 2.1 m high 23.5 degree ramp, sail across a 8 m wide pool filled with hungry crocodiles, and land at ground level on the other side. He has done this stunt many times and approaches it with confidence. Unfortunately, the motorcycle engine dies just as he starts up the ramp. He is going 12 m/s at that instant, and the rolling friction of his rubber tires (coefficient 0.02) is not negligible. Does he survive or does he become crocodile food? First of all, what is his speed as he leaves the ramp? What is his final horizontal distance from the far edge of the pool? Use a positive number if he makes it or a negative number if he becomes crocodile food.

Explanation / Answer

acceleration of motorcycle on the ramp

a=g(sino+ucoso)

a=9.81*(sin23.5+0.02cos23.5)=4.1 m/s2

From

V2=Vo2+2ad =122+2*(-4.1)*(2.1sin23.5)

V=10.04 m/s

Therfore

Vx=10.04cos23.5=9.21 m/s

Vy =10.04sin23.5=4 m/s

From

Y=Yo+Voyt-(1/2)gt2

0=2.1+4t-(1/2)*9.8*t2

4.9t2-4t-2.1=0

t=1.18 s

Horizontal distance travelled

X=Vxt =9.21*1.18

X=10.86 m

Since X>8 m,He will survive

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