Theory question 115
DynamicsA particle is projected vertically upwards from the ground with speeed 30 ms−1. Calculate the: (a) maximum height reached by the particle; (b) time taken by the particle to return to the ground; (c) time(s) taken for the particle to attain a height of 40 m above the ground. [Take g = 10 ms−2]
Show the model answer
Model answer
h = 30t − 5t².
(a) Top when v = 30 − 10t = 0, t = 3 s: h = 90 − 45 = 45 m.
(b) h = 0 again at t = 6 s.
(c) 30t − 5t² = 40 gives t² − 6t + 8 = 0: t = 2 s (going up) and t = 4 s (coming down).
Explanation
The particle passes 40 m twice, once each way.