Question

A cyclist reaches the bottom of a hill with a speed of 18 m/s. Neglecting air resistance and other friction, to what maximum height can they coast up the hill without pedalling? a) 19 m b) 20 m c) 17 m d) 18 m

Answer 1

Answer:

c) 17 m

Explanation:

From the conservation of energy.

Change in kinetic energy= change in potential energy

Now,

$\Delta KE=\Delta PE$

Now according to the situation.

$\frac{1}{2}mv^{2}=mgh\\h=\frac{v^{2} }{2g}$

Here, v is the velocity, m is the mass of an object, h is the height, g is the acceleration due to gravity.

Given that the speed of the bicycle is

$v=18m/s$

And the acceleration due to gravity is

$g=9.8 m/s^{2}$

Substitute these values.

$h=\frac{18^{2} }{2\times 9.8}\\h=16.53m$

Which means it is equivalent to 17 m

Therefore, the maximum height is 17 m