A-LevelMathematicsMechanics9709/51 · May/June 2019 · Q48 Marks
A small ball is projected with speed 25 m s¯¹ at an angle of 30° above the horizontal from a point O on horizontal ground. At time t s after projection the horizontal and vertically upwards displacements of the ball 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 x for the position of the ball when its path makes an angle of 15° below the horizontal.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [B1] Use horizontal motion
- [B1] Use vertical motion
- [M1] Eliminate t
- [A1] y = (x/√3) - (4x² / 375) or y = 0.577x - 0.0107x²
- [M1A1] Differentiate the equation from part (i) to find the gradient
- [M1] Attempt to solve
- [A1] x = 39.6 or x = 39.5
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