Which of the following is required for the conservation of momentum in a system of colliding objects?

The ball falls from rest ($v_0 = 0$) from a height $h_1 = 4.9 \, \text{m}$.
Using the kinematic equation $h = v_0 t + \frac{1}{2}gt^2$:

Using $v = v_0 + gt$:

The coefficient of restitution $e = 0.75$ is given by $e = \frac{v_1'}{v_1}$.

This is the initial upward velocity for the second bounce.

The time to reach the peak height after bouncing is $t_{up} = \frac{v_1'}{g}$.

The total time for the ball to go up and come back down to the surface for the second hit is $t_2 = 2 \cdot t_{up}$.

Total time = $t_1 + t_2 = 1 \, \text{s} + 1.5 \, \text{s} = 2.5 \, \text{s}$.

• Answer: (C) $\boxed{\text{2.5 sec}}$

48.

Kinetic energy: $KE = \frac{1}{2}mv^2$
Momentum: $p = mv$

From $p = mv$, we get $v = \frac{p}{m}$. Substitute this into the kinetic energy formula:

Taking the square root of both sides:

So, the ratio of their momentum is $\sqrt{m_1} : \sqrt{m_2}$.

• Answer: (A) $\boxed{\sqrt{m_1} : \sqrt{m_2}}$

49. An inelastic collision is characterized by the conservation of momentum, but the kinetic energy of the system is not conserved. Some kinetic energy is converted into other forms of energy, such as heat, sound, or deformation.

• Answer: (D) momentum is conserved but kinetic energy is not conserved