Question

2.A bike rider approaches a hill with a speed of 8.5m/s. The total mass of the bike and rider is 85kg.
a.Find the kinetic energy of the bike and rider before going up the hill.
b.The rider coasts up the hill. Assuming there is no friction, at what height will the bike come to a stop?
c.Does your answer depend on the mass of the bike and rider? Explain.

Answer 1

Solution:

A)

Kinetic energy = $\tfrac{mv^{2}}{2}$

K.E = $\tfrac{85 * 8.5^{2}}{2}=3070.62J=3.07kJ$

B)

Gain in Potential energy = Loss in Kinetic energy

$mgh= \tfrac{mv^{2}}{2}$

$height= \tfrac{v^{2}}{2g}$

$height= \tfrac{8.5^{2}}{2*9.81} =3.68m$

C)

In part A, the answer depends on the total mass of the bike and the rider, as Kinetic energy = $\tfrac{mv^{2}}{2}$ .In part B, the answer does not depend on the mass of the bike and the rider, because m is canceled on the both sides. m disappears in the equation:height = $\tfrac{v^{2}}{2g}$ .