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A rigid ball of mass m strikes a rigid wall at 60° and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall on the ball will be:
A
$\frac{mV}{2}$
B
$\frac{mV}{3}$
C
mV
D
2mV
Explanation
Only the normal component reverses: $2mV\cos60^\circ$.
Detailed Solution
$\Delta\vec{V} = \vec{V}_f - \vec{V}_i = (-V\cos60^\circ\hat{i} - V\sin60^\circ\hat{j}) - (V\cos60^\circ\hat{i} - V\sin60^\circ\hat{j})$
$\Delta\vec{V} = -2V\cos60^\circ\hat{i}$
Impulse $I = |\Delta\vec{P}| = m|\Delta\vec{V}| = m(2V\cos60^\circ) = mV$