Theory question 115
Dynamics(a) A girl threw a stone horizontally with a velocity of 30 ms−1 from the top of a cliff 50 m high. How far from the foot of the cliff does the stone strike the ground? [Take g = 10 ms−2]
(b) A body A, of mass 2 kg is held in equilibrium by means of two strings AP and AR. AP is inclined at 56° to the upward vertical and AR is horizontal. Find the tensions T1 and T2 in the strings. [Take g = 10 ms−2]
Show the model answer
Model answer
(a) Fall time: 50 = 5t², t = √10 ≈ 3.16 s. Horizontal distance = 30 × 3.16 ≈ 94.9 m.
(b) Vertically: T₁ cos 56° = 20, so T₁ ≈ 35.8 N.
Horizontally: T₂ = T₁ sin 56° = 20 tan 56° ≈ 29.7 N.
Explanation
Horizontal and vertical motion are independent; resolve the tensions in two directions.