Answer to Question #81999 in Physics for Ali ashraf wahbi

Question

A ball moving horizontally 3 m/s rolls of the top of a flight of stairs.If each stair is 0.5 m high and 0.5 wide, which stair will the ball hit?

Answer 1

In order to determine which step the ball lands on, the ball must fall at least a distance equal to its horizontal displacement.

t_1 =x_1/v_x =0.5/3 = 0.17 s,

y_1= (1/2)at_1^2=1/2 (9.8) (0.5/3)^2 = 0.14 m.

So the ball goes past the first step.

t_4 =x_1/v_x =4 0.5/3 = 0.67 s,

y_4= (1/2)at_4^2=1/2 (9.8) (4 0.5/3)^2= 2.18 m.

x_4=4(0.5)=2 m<y_4=2.18.

So the ball lands on the fourth step.