A ball rolls off the top of stairway with a horizontal velocity of magnitude 1.8 m/s. The steps are 0.20 m high and 0.20 m wide. Which step will the ball hit first?

Question

A ball rolls off the top of stairway with a horizontal velocity of magnitude 1.8 m/s. The steps are 0.20 m high and 0.20 m wide. Which step will the ball hit first? (A) First (B) Second (C) Third (D) Fourth

Tardigrade Admin · Accepted Answer

Given, x=0.20 m, y=0.20 m, u=1.8 m/s. Let the ball strikes the nth step of stairs, Vertical distance travelled =n y=n × 0.20=(1/2) g t2 Horizontal distance travelled, n x=u t or t=(n x/u) ∴ n y=(1/2) g × (n2 x2/u2) or n=(2 u2/g) (y/x2)=(2 ×(1.8)2 × 0.20/9.8 ×(0: 20)2)=3.3 ≈ 4

Q. A ball rolls off the top of stairway with a horizontal velocity of magnitude 1.8m/s. The steps are 0.20m high and 0.20m wide. Which step will the ball hit first?

First

Second

Third

Fourth

Given, x=0.20m,y=0.20m,u=1.8m/s. Let the ball strikes the nth step of stairs, Vertical distance travelled =ny=n×0.20=21​gt2 Horizontal distance travelled, nx=ut or t=unx​ ∴ny=21​g×u2n2x2​ or n=g2u2​x2y​=9.8×(0:20)22×(1.8)2×0.20​=3.3≈4

Q. A ball rolls off the top of stairway with a horizontal velocity of magnitude $1.8 m / s$ . The steps are $0.20 m$ high and $0.20 m$ wide. Which step will the ball hit first?