Standard +0.3 This is a standard M3 impulse-momentum problem requiring resolution in two perpendicular directions and use of given trigonometric information. While it involves multiple steps (resolving components, using Pythagoras, finding angles), the method is routine for this topic with no novel insight required. Slightly easier than average due to the given sin α value simplifying calculations.
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A ball of mass 0.6 kg is moving with speed \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a straight line. It is struck by an impulse \(I \mathrm { Ns }\) acting at an acute angle \(\theta\) to its direction of motion (see diagram). The impulse causes the direction of motion of the ball to change by an acute angle \(\alpha\), where \(\sin \alpha = \frac { 8 } { 17 }\). After the impulse acts the ball is moving with a speed of \(3.4 \mathrm {~ms} ^ { - 1 }\). Find \(I\) and \(\theta\).
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\includegraphics[max width=\textwidth, alt={}, center]{dfe477d4-eae6-40e1-b704-1a97485f4c7e-2_477_534_261_770}
A ball of mass 0.6 kg is moving with speed $1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in a straight line. It is struck by an impulse $I \mathrm { Ns }$ acting at an acute angle $\theta$ to its direction of motion (see diagram). The impulse causes the direction of motion of the ball to change by an acute angle $\alpha$, where $\sin \alpha = \frac { 8 } { 17 }$. After the impulse acts the ball is moving with a speed of $3.4 \mathrm {~ms} ^ { - 1 }$. Find $I$ and $\theta$.
\hfill \mbox{\textit{OCR M3 2013 Q1 [5]}}