A-LevelMathematicsMechanics9709/41 · Oct/Nov 2024 · Q510 Marks
A particle, A, is projected vertically upwards from a point O with a speed of 80 ms⁻¹. One second later a second particle, B, with the same mass as A, is projected vertically upwards from O with a speed of 100 ms⁻¹. At time T s after the first particle is projected, the two particles collide and coalesce to form a particle C.
- (a)Show that T = 3.5 .[4]
- (b)Find the height above O at which the particles collide.[1]
- (c)Find the time from A being projected until C returns to O.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- *M1 s_A = 80T - (1/2)gT² OR s_B = 100(T-1) - (1/2)g(T-1)²
- A1 Two correct expressions for the displacement of both particles at time T
- DM1 100(T – 1) – 5(T – 1)² = 80T – 5T²
- A1 Leading to T = 3.5
- B1 [s=80×3.5-(1/2)g×3.5²]=218.75m
- *M1 v_A = 80-g×3.5 [=45] OR v_B = 100-g×2.5 [=75]
- DM1 45m+75m= 2mv
- A1 v = 60
- DM1 -218.75=60t-(1/2)g×t²
- A1 t=14.9+3.5 =18.4s
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