Moderate -0.8 This is a straightforward two-step mechanics problem requiring only basic impulse-momentum formula (impulse = change in momentum) and the coefficient of restitution formula (v = eu). No problem-solving insight needed—just direct application of standard formulas with simple arithmetic.
1 A small smooth sphere \(P\) of mass \(2 m\) is at rest on a smooth horizontal surface. A horizontal impulse of magnitude \(8 m u\) is given to \(P\). Subsequently \(P\) collides directly with a fixed smooth vertical barrier at right angles to \(P\) 's direction of motion. Given that the coefficient of restitution between \(P\) and the barrier is 0.75 , find the speed of \(P\) after the collision.
Equate impulse to momentum to find initial speed \(v\) and Newton's law of restitution to find new speed
# Question 1:
| $v = 4u$, $v' = ev = [-]3u$ | M1 A1 | Equate impulse to momentum to find initial speed $v$ and Newton's law of restitution to find new speed |
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1 A small smooth sphere $P$ of mass $2 m$ is at rest on a smooth horizontal surface. A horizontal impulse of magnitude $8 m u$ is given to $P$. Subsequently $P$ collides directly with a fixed smooth vertical barrier at right angles to $P$ 's direction of motion. Given that the coefficient of restitution between $P$ and the barrier is 0.75 , find the speed of $P$ after the collision.
\hfill \mbox{\textit{CAIE FP2 2014 Q1 [2]}}