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 at26.5° 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 2.30 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?
(b) What is the speed of the boat when it strikes the water again? Neglect any effects due to air resistance.

Explanation / Answer

Here,

mass , m = 285 kg

theta = 26.5 degree

speed , v = 13.5 m/s

coefficient of friction , u = 0.150

height , h = 2.3 m

a) let the speed of boat is v

Using conseravtion of energy

0.5 * 285 * (v^2 - 13.5^2) = -285 * 9.8 * 2.30 - 0.150 * 9.8 * 285 * (2.3/sin(26.5))

solving for v

v = 11.05 m/s

the speed of boat at the top is 11.05 m/s

b) at the water surface , let the speed is vf

Using conseravtion of energy

0.5 * 285 * (vf^2 - 11.05^2 ) = 9.8 * 285 * 2.30

solving for vf

vf = 12.93 m/s

the speed of boat will be 12.93 m/s

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