O-LevelAdditional MathematicsVectors in two dimensions4037/11 · May/June 2019 · Q57 Marks
A particle P is moving with a velocity of 20ms⁻¹ in the same direction as (3/4).
- (i)Find the velocity vector of P.[2]
- (ii)At time t = 0s, P has position vector (1/2) relative to a fixed point O. Write down the position vector of P after t s.[2]
- (iii)A particle Q has position vector (17/8) relative to O at time t = 0s and has a velocity vector (8/12) ms⁻¹. Given that P and Q collide, find the value of t when they collide and the position vector of the point of collision.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [M1] finding and using the magnitude of (3/4)
- [A1] v = (12/16)
- [M1] correct use of position vector and their velocity vector
- [A1] rp = (1/2) + (12/16)t
- [M1] equating position vectors of both particles at time t and solve either equation for t
- [A1] t = 4
- [A1] Position vector of collision = (49/66)
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