Question

A girl at rest at gate of her society which 3.2m above the road comes drawn the slope AB on a cycle without paddling [g=10N/kg]. Find the velocity with which girl reaches the road​

Answer 1

In these type of questions, where the angle of the slope is not provided, always apply the following method:

• The WORK-ENERGY THEOREM states that the total work done by all the forces on an object will be equal to the change in kinetic energy.

So, here the force doing work is gravity.

$F_{g}=\Delta KE$

$\implies mgh= \dfrac{1}{2} m {v}^{2} - \dfrac{1}{2} m {0}^{2}$

$\implies mgh= \dfrac{1}{2} m {v}^{2}$

$\implies gh= \dfrac{1}{2} {v}^{2}$

$\implies {v}^{2} = 2gh$

$\implies v = \sqrt{2gh}$

$\implies v = \sqrt{2 \times 10 \times 3.2}$

$\implies v = \sqrt{64}$

$\implies v = 8 \: m {s}^{ - 1}$

So, velocity of the cycle upon reaching the road is 8 m/s.