Question

# A ball moving with a momentum of $5kgm/s$ strikes against a wall at an angle of $45°$ and is deflected at the same angle. Calculate the change in momentum.

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Solution

## Step 1: Given DataMomentum $p=5kgm/s$Angle of deflection $\theta =45°$Step 2: ExplanationLet us divide the momentum into its components, and consider the $p\mathrm{cos}\theta$ as shown in the figure.From the figure, we see that the cosine component of the momentum undergoes no change.Therefore the change in momentum along the wall is zero.So, the actual change in moment occurs due to the sine component of the momentum.According to the figure, the momentum after bouncing back goes in the opposite direction.Step 3: Calculate the Change in MomentumTherefore, a change in momentum $∆p=-p\mathrm{sin}\theta -p\mathrm{sin}\theta$ $=-2p\mathrm{sin}\theta$ $=-2×5×\mathrm{sin}45°$ $=-2×5×\frac{1}{\sqrt{2}}$ $=-7kgm/s$Hence, the change in momentum is $7kgm/s$ in the opposite direction.

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