Question

Person A throws a stone of mass m with initial velocity v, at an angle 0 with the horizontal from a bridge that is H meters above the water level. At the same instant, Person B throws a stone of mass 2m with the same initial velocity in the horizontal direction as shown below. Which of the following is correct for the speeds of each stone V and Va for the time t and tn, respectively, when they strike the water? 0 water level

Answer 1

By energy conservation, the change in gravitational potential is same for both, thus, change in kinetic energy is also the same which in turn implies same final speed if initial is same.(Note that masses will cancel out)

So ,

$V_A=V_B$

For time

$-H=v_0\sin\theta t_A-\frac{1}{2}gt^2_A$

$\frac{1}{2}gt^2_A-v_0\sin\theta t_A-H=0$

$t_A=\frac{v_0\sin\theta}{g}+\sqrt{\frac{v^2_0\sin^2\theta}{g^2}+\frac{2H}{g}}$

where as

$t_B=\sqrt{\frac{2H}{g}}$

Clearly, $t_B<t_A$