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Nov 2010 p41 q1
3872
Two particles P and Q move vertically under gravity. The graphs show the upward velocity v m s-1 of the particles at time t s, for 0 ≤ t ≤ 4. P starts with velocity V m s-1 and Q starts from rest.
Find the value of V.
\(Given that Q reaches the horizontal ground when t = 4, find\)
the speed with which Q reaches the ground,
the height of Q above the ground when t = 0.
Solution
(i) For particle P, using the equation of motion under gravity:
\(0 = V - gt\)
\(At t = 2 s, the velocity is zero, so:\)
\(0 = V - g \times 2\)
Solving for V gives:
\(V = 2g\)
\(Assuming g = 10 m s-2, we find:\)
\(V = 20 \text{ m s}^{-1}\)
(ii) For particle Q, using the equation of motion:
\(v = u + gt\)
\(Since Q starts from rest, u = 0, and at t = 4 s:\)
\(v = 0 + 10 \times 4 = 40 \text{ m s}^{-1}\)
(iii) The height h from which Q was dropped can be found using: