Question

A school bus is traveling at a velocity of 20.0 km/h [N] relative to the ground. A student on the bus walks at a speed of 2.0 km/h relative to the bus. Determine the velocity of the student relative to the ground if he: a) walks towards the back of the bus b) walks towards the front of the bus

Answer 1

Given,

The velocity of the bus, v=20.0 km/h

The velocity of the student relative to the bus, u=2.0 km/h

a.

The velocity of the student relative to the ground, when he is traveling in the direction opposite to the direction of the bus, i.e., towards the back of the bus, is given by the difference between the velocity of the bus and his own velocity relative to the bus.

Therefore student's velocity relative to the ground is given by,

`v_b=v-u`

On substituting the known values,

`\begin{gathered} v_b=20-2 \\ =18\text{ km/h} \end{gathered}`

Thus the velocity of the student relative to the ground when he walks towards the back of the bus is given by 18 km/h

b.

When the bus and the student are traveling in the same direction, the student's velocity relative to the ground will be given by the sum of the velocities.

Thus, the students velocity is given by.

`v_f=v+u`

On substituting the known values,

`\begin{gathered} v_f=20+2 \\ 22\text{ km/h} \end{gathered}`

The velocity of the student relative to the ground, when he walks towards the front of the bus is 22 km/h.