A-LevelMathematicsMechanics9709/51 · Oct/Nov 2018 · Q79 Marks
A small object is projected with speed 24 m s¯¹ from a point O at the foot of a plane inclined at 45° to the horizontal. The angle of projection of the object is 15° above a line of greatest slope of the plane (see diagram). At time t s after projection, the horizontal and vertically upwards displacements of the object from O are x m and y m respectively.
- (i)Express x and y in terms of t, and hence find the value of t for the instant when the object strikes the plane.[4]
- (ii)Express the vertical height of the object above the plane in terms of t and hence find the greatest vertical height of the object above the plane.[5]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [B1] x = (24cos60)t (Use horizontal motion)
- [B1] y = (24sin60)t – gt²/2 (Use vertical motion)
- [M1] (24cos60)t = (24sin60)t -gt²/2 (Recognise that x = y)
- [A1] t = 1.76
- [B1] h = (24sin60)t – gt²/2 – (24cos60)t
- [M1] dh/dt = 24(sin60 - cos60) - gt (Attempt to differentiate)
- [M1] 24(sin60 - cos60) – gt = 0 (Equate dh/dt = 0 to find t)
- [A1] t = 0.878(46..)
- [A1] h = 3.86 m
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