Question

Two balls, A and B, are thrown simultaneously, A vertically upward with a speed of 20 m/s from the ground and B vertically downward from a height of 40 m with the same speed and along the same line of motion. At what points do the two balls collide by taking acceleration due to gravity as 9.8 $m/s^2$?

• A. The balls will collide after 3s at a height of 30.2 m from the ground
• B. The balls will collide after 2s at a height of 20.1 m from the ground
• C. The balls will collide after Is at a height of 15.1 m from the ground
• D. The balls will collide after 5s at a height of 20 m from the ground

Answer 1

The correct option is C The balls will collide after Is at a height of 15.1 m from the ground

let the accelerations of both ball be $a_A=-g,a_B=-g$

and let the velocities be $v_A=20m/s,v_b=-20m/s$

relative acceleration=$a_A-a_B=0$

relative velocity=$v_A-v_B=40m/s$

$s=ut+\frac{1}{2}a{t}^2$

$s=40m,u=40m/s,a=0$

$\therefore t=\frac{s}{v}=\frac{40}{40}=1s$

For distance from ground we will observe particle A

$s=ut+\frac{1}{2}a{t}^2$

$v=20m/s,t=1s,a=-g=-9.8m/s^2$

$s=20-\frac{1}{2}\times 9.8\times 1^2=15.1m$