A-LevelMathematicsMechanics9709/52 · Oct/Nov 2017 · Q711 Marks
A small ball B is projected from a point O which is h m above a horizontal plane. At time 2s after projection B has speed 18 m s⁻¹ and is moving in the direction 30° above the horizontal.
- (i)Find the initial speed and the angle of projection of B.[4]
- (ii)B has speed 38 m s⁻¹ immediately before it strikes the plane. Calculate h.[2]
- (iii)B bounces when it strikes the plane, and leaves the plane with speed 20 m s⁻¹ but with its horizontal component of velocity unchanged. Find the total time which elapses between the initial projection of B and the instant when it strikes the plane for the second time.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [B1] UH=18cos30 and UV =18sin30 + 2g(=29)
- [M1] Uses Pythagoras's Theorem and trigonometry.
- [A1] U = 32.9(24..) ms⁻¹
- [A1] θ = 61.7°
- [M1] Uses 2 ways to find v, the vertical velocity at the ground and equates.
- [A1] h = 18
- [M1] Uses v = u + at for first part of flight.
- [A1] t = 6.36(6)
- [M1] Uses v = u + at for second part of flight.
- [A1] t' = 2.50(6)
- [A1] T (= 6.366 +2.506) = 8.87
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