A ball of mass 0.5 kg is dropped from a height of 40 m . The ball...

A ball of mass 0.5 kg is dropped from a height of 40 m . The ball hits the ground and rises to a height of 10 m . The impulse imparted to the ball during its collision with the ground is (Take

\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2

)

Options

A21 NS
B7 NS
C0
D84 NS

Correct answer

A. 21 NS

Step-by-step solution

\begin{aligned} v_i & =-\sqrt{2 \mathrm{gh}_i}=-\sqrt{2 \times 9.8 \times 10}=-28 \mathrm{~m} / \mathrm{s} \\ \mathrm{v}_{\mathrm{f}} & =\sqrt{2 \mathrm{gh}_{\mathrm{i}}}=\sqrt{2 \times 9.8 \times 10}=14 \mathrm{~m} / \mathrm{s} \\ \overrightarrow{\mathrm{I}} & =\Delta \overrightarrow{\mathrm{P}}=\mathrm{m} \overrightarrow{\mathrm{v}}_{\mathrm{f}}-\mathrm{m} \overrightarrow{\mathrm{v}}_{\mathrm{i}} \\ & =\mathrm{m}\left[\overrightarrow{\mathrm{v}}_{\mathrm{f}}-\overrightarrow{\mathrm{v}}_{\mathrm{i}}\right]=0.5[14-(-28)] \\ & =0.5 \times 42=21 \mathrm{NS} \end{aligned}

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