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

c) 17 m

Step-by-step explanation:

From the conservation of energy.

Change in kinetic energy= change in potential energy

Now,

`\Delta KE=\Delta PE`

Now according to the situation.

`(1)/(2)mv^(2)=mgh\\h=(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=(18^(2) )/(2* 9.8)\\h=16.53m`

Which means it is equivalent to 17 m

Therefore, the maximum height is 17 m