A ball is projected vertically up from ground.
Boy A standing at the window of first floor of a nearly building observes that the time interval between tha ball crossing him while going up and the ball crossing him while going down is 2s. Another boy B standing on the second floor notices that time interaval between the ball passing him twice, during up motion and down motion is 1 s. Calculate the difference between the vertical positions of boy B and boy A (Assume , acceleration due to gravity , `g=10 m//s^2` )

Options

A. 8.45 m
B. 3.75 m
C. 4.25 m
D. 2.50 m

Answer

B

Explanation

The figure given below, shows the vertical motion of a ball,

Here, ball crosses the 1st floor in 2s , so it goes up in 1s and goes down in next one second. So, `v-v_A=-"gt"`
`rArr 0-v_A =-10(1) rArr V_A= 10 m//s`
`because` Boy, Bobserved the ball crossing him while up and down motion is 1s. so, time taken by the ball to reached the floor B from floor A is 0.5 s.
So, `s=V_A t -1/2 "gt"^2`
`rArr =10 xx 0.5 -1/2 xx10 xx(0.5)^2`
`=5-1.25 =3.75 m`