(a)[3]
Show that the value of $c$ is $80$.
(b)[3]
Find the speed at which the motorcyclist travels up the hill when the motion is steady.
Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A motorcycle engine can deliver a peak power of $105\text{ kW}$. The combined mass of the motorcycle and its rider is $400\text{ kg}$. The overall resistive force acting on the motorcycle and rider is $cv\text{ N}$, where $v\text{ m s}^{-1}$ denotes the motorcyclist’s speed and $c$ is constant. The motorcyclist moves along a straight horizontal road at maximum engine power. At a speed of $35\text{ m s}^{-1}$, his acceleration is $0.5\text{ m s}^{-2}$. He then climbs a straight hill while still using maximum engine power. The hill is inclined at $\sin^{-1}\!\left(\frac{3}{20}\right)$ to the horizontal.