A-LevelMathematicsMechanics9709/53 · Oct/Nov 2019 · Q47 Marks
A small ball B is projected with speed 30 m s⁻¹ at an angle of 60° above the horizontal from a point O. At time t s after projection the horizontal and vertically upwards displacements of B from O are x m and y m respectively.
- (i)Express x and y in terms of t and hence find the equation of the trajectory of the ball.[4]
- (ii)Find the value of x for which OB makes an angle of 45° above the horizontal.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [B1] x = 30cos60t
- [B1] y = 30sin60t - gt²/2
- [M1] y = (30sin60x) / (30cos60) - (5x²) / (30cos60)²
- [A1] y = 1.73x - 0.0222x² or y = √3x - x²/45
- [M1] x = y or tan 45 = y/x
- [M1] 1 = 1.73 - 0.0222x or 1 = √3 - x/45
- [A1] x = 32.9
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