Question

Two balls were thrown vertically upwards with different velocities, what is the shape of the graph between distance between the balls and time before either of the two collide with ground?

• A. Straight line passing through origin
• B. Parabola
  
• C. Circle
• D. None of the above
  

Answer 1

The correct option is A Straight line passing through origin

Let the initial velocity of the balls be $u_1$ and $u_2$ (upwards) respectively.

Also the acceleration of the balls $a_1=-g$ $a_2=-g$

$\therefore$ Relative acceleration of ball 1 w.r.t 2 $a_{12}=a_1-a_2=0$

Initial velocity of 1 w.r.t 2 $u_{12}=u_1-u_2$ (upwards)

Using $S_{12}=u_{12}t-\frac{a_{12}{t}^2}{2}$

$\therefore$ Distance between them $S_{12}=(u_1-u_2)t$

Thus S-t graph will be a straight line having a slope $(u_1-u_2)$ passing through origin.