A 285-kg stunt boat is driven on the surface of a lake at a constant speed of 13

Question

A 285-kg stunt boat is driven on the surface of a lake at a constant speed of 13.5 m/s toward a ramp, which is angled at 21.3°above the horizontal. The coefficient of friction between the boat bottom and the ramp's surface is 0.150, and the raised end of the ramp is 1.60 m above the water surface.

(a) Assuming the engines are cut off when the boat hits the ramp, what is the speed of the boat as it leaves the ramp?

___________m/s

(b) What is the speed of the boat when it strikes the water again? Neglect any effects due to air resistance.

___________m/s

Explanation / Answer

a)

let the speed of boat when it leaves the ramp is v

Using work energy theorum

change in kinetic energy = net work done

0.5 * 285 * (v^2 - 13.5^2) = - 285 * 9.8 * 1.6 - 0.15 * 285 * 9.8 * (1.6/sin(21.3))

solving for v

v = 11.74 m/s

the speed of boat when it leaves the ramp is 11.74 m/s

b)

for the speed of boat when it hits the water again is vf

Using third equation of motion

vf^2 - v^2 = 2 * a * h

vf^2 - 11.74^2 = 2 * 9.8 * 1.6

vf = 13 m/s

the speed of boat when it strikes the water again is 13 m/s

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