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4 Unit A2 2: Applied Mathematics (A-level only)

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Question 26

The points X X\,X and Y Y\,Y lie 100 m apart on horizontal ground. At time t=0t = 0t=0 two balls, M M\,M and NNN, are projected from X X\,X and Y Y\,Y respectively. Ball M M\,M is projected with speed 30 ms-1 at an angle of 45∘ 45^\circ\,45∘ to the horizontal. Ball N N\,N is projected with speed U ms−1U \text{ ms}^{-1}U ms−1 at an angle of ϕ \phi\,ϕ to the horizontal. At time t=2.5t = 2.5t=2.5, the balls collide in mid-air. Both balls are assumed to be particles in free flight.

a.

Find the velocity of M M\,M the instant before it collides with NNN.

[6]
bi.

Find the size of angle ϕ\phiϕ.

[6]
bii.

Find the value of UUU.

[6]
c.

State one limitation of the model that could affect the accuracy of your answers.

[1]
Markscheme

4 Unit A2 2: Applied Mathematics (A-level only) Questions

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