Given impulse with vector deflection

A particle receives an impulse (often in vector form) that deflects its motion through a given angle; find the impulse magnitude, velocity components, or deflection angle using vector methods.

6 questions · Standard +0.3

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Edexcel FM1 2019 June Q3
9 marks Challenging +1.2
  1. A particle \(P\), of mass 0.5 kg , is moving with velocity ( \(4 \mathbf { i } + 4 \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\) when it receives an impulse I of magnitude 2.5 Ns.
As a result of the impulse, the direction of motion of \(P\) is deflected through an angle of \(45 ^ { \circ }\) Given that \(\mathbf { I } = ( \lambda \mathbf { i } + \mu \mathbf { j } )\) Ns, find all the possible pairs of values of \(\lambda\) and \(\mu\).
Edexcel FM1 2020 June Q1
7 marks Moderate -0.5
  1. A particle \(P\) of mass 0.5 kg is moving with velocity ( \(4 \mathbf { i } + 3 \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\) when it receives an impulse \(\mathbf { J }\) Ns. Immediately after receiving the impulse, \(P\) is moving with velocity \(( - \mathbf { i } + 6 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
    1. Find the magnitude of \(\mathbf { J }\).
    The angle between the direction of the impulse and the direction of motion of \(P\) immediately before receiving the impulse is \(\alpha ^ { \circ }\)
  2. Find the value of \(\alpha\)
Edexcel FM1 2021 June Q4
8 marks Standard +0.3
  1. A particle \(P\) has mass 0.5 kg . It is moving in the \(x y\) plane with velocity \(8 \mathbf { i } \mathrm {~ms} ^ { - 1 }\) when it receives an impulse \(\lambda ( - \mathbf { i } + \mathbf { j } )\) Ns, where \(\lambda\) is a positive constant.
The angle between the direction of motion of \(P\) immediately before receiving the impulse and the direction of motion of \(P\) immediately after receiving the impulse is \(\theta ^ { \circ }\) Immediately after receiving the impulse, \(P\) is moving with speed \(4 \sqrt { 10 } \mathrm {~ms} ^ { - 1 }\)
Find (i) the value of \(\lambda\)
(ii) the value of \(\theta\)
Edexcel FM1 2022 June Q3
5 marks Standard +0.3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{86a37170-046f-46e5-9c8c-06d5f98ca4fe-10_302_442_244_813} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A particle \(P\) of mass 0.5 kg is moving in a straight line with speed \(2.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it receives an impulse of magnitude 3 Ns .
The angle between the direction of motion of \(P\) immediately before receiving the impulse and the line of action of the impulse is \(\alpha\), where \(\tan \alpha = \frac { 4 } { 3 }\), as shown in Figure 2. Find the speed of \(P\) immediately after receiving the impulse.
Edexcel FM1 2023 June Q1
6 marks Standard +0.3
  1. A particle \(P\) of mass 2 kg is moving with velocity \(( - 4 \mathbf { i } + 3 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) when it receives an impulse \(( - 6 \mathbf { i } + 42 \mathbf { j } )\) N s.
    1. Find the speed of \(P\) immediately after receiving the impulse.
    The angle through which the direction of motion of \(P\) has been deflected by the impulse is \(\alpha ^ { \circ }\)
  2. Find the value of \(\alpha\)
Edexcel FM1 Specimen Q1
6 marks Standard +0.3
  1. A particle \(P\) of mass 0.5 kg is moving with velocity \(( 4 \mathbf { i } + \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) when it receives an impulse \(( 2 \mathbf { i } - \mathbf { j } )\) Ns.
Show that the kinetic energy gained by \(P\) as a result of the impulse is 12 J .