(i)[3]
Show that, during the upward motion of the ball, $\left(\frac{500}{v+500}-1\right)\frac{dv}{dx}=0.02$.
(ii)[3]
Find the ball’s greatest height above its point of projection.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
A ball of small mass $m\,\text{kg}$ is fired straight upward at a speed of $14\,\text{m s}^{-1}$. When it is $x\,\text{m}$ above the launch point, its upward velocity is $v\,\text{m s}^{-1}$. During the ascent, a resisting force of magnitude $0.02mv\,\text{N}$ acts on the ball.
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This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies Newton’s second law in the form $m v \dfrac{dv}{dx} = -mg - 0.02mv$” …
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