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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 225

A golf ball is struck from a point O O\,O on level ground. Its position t t\,t seconds after being struck is modelled by

x=20tcos⁡αx = 20t\cos\alphax=20tcosα, y=20tsin⁡α−4.9t2y = 20t\sin\alpha - 4.9t^2y=20tsinα−4.9t2

where x x\,x metres and y y\,y metres are the horizontal and vertical displacements from OOO, and α \alpha\,α is the angle of projection above the horizontal.

a.

Show that a Cartesian equation for the path of the ball is

y=xtan⁡α−49x2sec⁡2α4000\displaystyle y = x\tan\alpha - \frac{49x^2\sec^2\alpha}{4000}y=xtanα−400049x2sec2α​

[4]
b.

Given that α=30°\alpha = 30°α=30°, find the horizontal distance travelled by the ball before it first returns to the ground. Give your answer to three significant figures.

[3]
c.

State one modelling assumption that has been made.

[1]
Markscheme

3 Unit A2 1: Pure Mathematics (A-level only) Questions

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