Question

A ball of mass 'm' is thrown vertically upward from the ground and reaches a height '2h' before momentarily coming to rest.If 'g' is acceleration due to gravity.what is the impulse received due to gravity force during its flight?(neglect air resistance).

Answer 1

Let
Initial velocity = u
Final velocity, v = 0
Displacement, s = 2h
​Acceleration, a = - g

​From the equations of motion,
$$\begin{gathered} v^2-u^2=2as \\ 0-u^2=2\left(-g\right)\left(2h\right) \\ u=\sqrt{4gh} \end{gathered}$$

Impulse:

$$\begin{gathered} I=m(v-u) \\ =m\left(0-\sqrt{4gh}\right) \\ =-m\sqrt{4gh} \\ =-2m\sqrt{gh} \end{gathered}$$

Magnitude of impulse, $I=2m\sqrt{gh}$