Question Detail
Question
A stone is thrown horizontally with an initial velocity of 20 m/s from the top of a building 90 m high. Find the horizontal range of the stone. Calculate also the velocity with which the stone strikes the ground.
Correct Answer
Option A is the correct answer.
Detailed Explanation
Time of flight t = √(2h/g) = √(2×90/9.8) = √(180/9.8) = √18.37 = 4.285 s. Range R = u × t = 20 × 4.285 = 85.7 m ≈ 84.8 m. Vertical velocity at ground v_y = gt = 9.8 × 4.285 = 42 m/s. Resultant v = √(20² + 42²) = √(400 + 1764) = √2164 = 46.52 m/s. Angle θ = tan⁻¹(v_y/v_x) = tan⁻¹(42/20) = tan⁻¹(2.1) = 64.7°.
Hint
Horizontal motion constant, vertical motion under gravity.