Question

Pankaj and Sudhir are playing with two different balls of masses m and 2m respectively. If Pankaj throws his ball vertically up and Sudhir at an angle $\theta$ with the vertical, both of them stay in our view for the same period. The height attained by the two balls are in the ratio

• A.
• B.
• C.
• D.

Answer 1

The correct option is B


Time of flight for the ball thrown by Pankaj $T_1=\frac{2u_1}{g}$
Time of flight for the ball thrown by Sudhir $T_2=\frac{2u_{2}sin({90}^{\circ }-\theta )}{g}=\frac{2u_{2}cos\theta }{g}$
According to problem $T_1=T_2\Rightarrow \frac{2u_1}{g}=\frac{2u_{2}cos\theta }{g}\Rightarrow u_1=u_{2}cos\theta$
Height of the ball thrown by Pankaj $H_1=\frac{u_1^2}{2g}$
Short Trick:
Maximum height $H\propto T^2$
$\frac{H_1}{H_2}={\left(\frac{T_1}{T_2}\right)}^2$
Height of the ball thrown by Sudhir $H_2=\frac{u_2^{2}si{n}^2({90}^{\circ }-\theta )}{2g}=\frac{u_2^{2}co{s}^2\theta }{2g}$
$\therefore \frac{H_1}{H_2}=\frac{\frac{u_1^2}{2g}}{\frac{u_2^{2}co{s}^2\theta }{2g}}[As{u}_1=u_{2}cos\theta ]$