Question

A stair of 50 steps each of 10cm a ball is dropped from 10th step reaches on earth with 2m/sec. If same ball reaches on earth with 4m/sec the step of stair is?

Answer 1

Steps to be covered = 10 steps

Each step = 10 cm

Distance to be covered = 10 * 10 = 100 cm = 1 m

V = u + at

2 = 0 + at

at = 2

u = 0 as dropped

a = a m/s²

t = time taken to reach ground

S = ut + (1/2)at²

1 = 0 + (1/2)at²

=> at² = 2

=> 2t = 2   ( putting at = 2)

=> t = 1

=> a * 1 = 2

=> a = 2  m/s²

now v = 4m/s

4 = 0 + at

4 = 2t

=> t = 2 sec

S = ut + (1/2)at²

S = 0 + (1/2)(2)(2)²

S = 4 m

4 m = 400 cm

Each step = 10 cm

400/10 = 40 step

from Step 40 ball need to be dropped

Answer 2

A ball is dropped from 10th step reaches on the earth with speed, v = 2m/s .

height of ball was , h = 10 × 10 cm = 1m

now, using formula, v² = u² + 2as

or, (2)² = 0 + 2a × 1

or, a = 2m/s²

case 2 : ball reaches on the earth with speed 4m/s

initial speed of ball, u = 0
final speed of ball, v = 4m/s

so, using formula , v² = u² + 2as

or, (4)² = 0 + 2×2 × s

or, s = 4m or 400cm

hence, total number of step of stair = 400cm/10cm = 40