A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s² and neglecting air resistance will give :
- (a)R = 12 m
- (b)R = 18 m
- (c)R = 24 m
- (d)R = 30 m
Correct — C, R = 24 m. Horizontal and vertical motions are independent. Vertically the stone starts with zero downward speed and falls the 20 m height under gravity: 20 = ½ × 10 × t², giving t² = 4, so t = 2 s. Horizontally there is no acceleration, so the stone keeps its launch speed of 12 m/s. The horizontal distance is R = speed × time = 12 × 2 = 24 m.
- (a)R = 12 m — This is just the launch speed (12 m/s) read as a distance, or the range for a 1-second fall. The stone is in the air for 2 s, so R = 12 × 2 = 24 m, not 12 m.
- (b)R = 18 m — This does not follow from the numbers; it would need a flight time of 1.5 s, but a 20 m fall under g = 10 m/s² takes 2 s, giving 24 m.
- (d)R = 30 m — This overestimates the flight time as 2.5 s. The correct time from 20 = ½ × 10 × t² is 2 s, so R = 24 m.
In projectile motion the horizontal and vertical motions are independent. A horizontally launched body keeps a constant horizontal velocity while it accelerates downward under gravity. The time in the air is fixed by the height of fall alone; the horizontal range is that time multiplied by the launch speed.
Solve it in two steps: first the fall time from h = ½gt² (the horizontal speed does not affect how long it falls), then the range R = uₓ × t. The height sets the clock; the horizontal speed sets the distance.
- For a horizontal launch, time of flight depends only on the height: t = √(2h/g).
- Here t = √(2 × 20 / 10) = √4 = 2 s.
- Horizontal velocity stays constant at 12 m/s (no horizontal force).
- Range R = horizontal speed × time = 12 × 2 = 24 m.
- Thinking a faster horizontal throw stays in the air longer — flight time depends only on the height.
- Using the wrong g, or forgetting to square the time in h = ½gt².
A body is thrown horizontally from a known height at a known speed and you find where it lands — get the fall time from the height, then multiply by the horizontal speed.
No directly related past PYQ was found.
- practice — not a real PYQ
A ball is thrown horizontally at 15 m/s from a 5 m high table (g = 10 m/s²). How far from the table's base does it land?
- (a)7.5 m
- (b)15 m
- (c)10 m
- (d)22.5 m
Answer(b) 15 m — fall time t = √(2 × 5 / 10) = 1 s, so R = 15 × 1 = 15 m.
- practice — not a real PYQ
Two stones are thrown horizontally from the same height, one at 10 m/s and the other at 20 m/s. They reach the ground:
- (a)at the same time
- (b)the faster one first
- (c)the slower one first
- (d)cannot be decided
Answer(a) at the same time — flight time depends only on the height of fall, not the horizontal speed.