Theory question 115
DynamicsAn object is thrown vertically upwards from the top of a building 20 m high. If the object passes the point it was thrown after 4 seconds on its way down, find the: (a) velocity at which the object was thrown; (b) time taken when the object is 10 m above the level it was thrown; (c) time taken when the object is 10 m below the level it was thrown; (d) velocity with which the object hits the ground. [Take g = 10 ms−2]
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Take up as positive: s = ut − 5t².
(a) s = 0 at t = 4: 4u − 80 = 0, u = 20 ms⁻¹.
(b) 20t − 5t² = 10: t² − 4t + 2 = 0, t = 2 ± √2 = 0.59 s (going up) and 3.41 s (coming down).
(c) 20t − 5t² = −10: t² − 4t − 2 = 0, t = 2 + √6 ≈ 4.45 s.
(d) v² = u² + 2as = 400 + 2(10)(20) = 800, v ≈ 28.3 ms⁻¹ downwards.
Measure displacement from the point of throwing; below it is negative.