Question

Hello, I am so confused about this problem, could you help ?

Answer 1

Given:

The masses of the balls, m₁=1 kg

m₂=2 kg

The height of 1 kg ball, h₁=6 m

The height of 2 kg ball, h₂=3 m

To find:

Which of the given statements are true?

Explanation:

From the law of conservation of energy, the energy can neither be created nor be destroyed. As the air resistance is negligible, the initial potential energy of the balls will be equal to their kinetic energy when they reach the ground.

Thus, the kinetic energy of the balls when they reach the ground is given by,

$KE=PE=mgh$

Where m is the mass of the balls, h is their respective height, and g is the acceleration due to gravity.

Thus the kinetic energy of mass m₁ is,

$\begin{gathered} KE_1=1\times9.8\times6 \\ =58.8\text{ J} \end{gathered}$

The kinetic energy of mass m₂ is,

$\begin{gathered} KE_1=2\times9.8\times3 \\ =58.8\text{ J} \end{gathered}$

The velocities of the balls will be given by the equation of kinetic energy.

Thus,

$KE=\frac{1}{2}mv^2$

Where v is the respective velocities of the balls when they reach the ground.

On rearranging the above equation, the velocities will be given by,

$v=\sqrt{\frac{2\times KE}{m}}$

On substituting the known values, the velocity of the mass m₁ is

$\begin{gathered} v_1=\sqrt{\frac{2\times58.8}{1}} \\ =10.84\text{ m/s} \end{gathered}$

The velocity of the mass m₂ is,

$\begin{gathered} v_2=\sqrt{\frac{2\times58.8}{2}} \\ =7.7\text{ m/s} \end{gathered}$

Thus the balls will have the same kinetic energies when they reach the ground. But the 1 kg ball will have a greater velocity than the 2-kg ball.

The time interval the ball takes is dependent on the height only and not on the mass. Thus the balls will not reach the ground at the same time.

Final answer:

Thus the correct answer is options are option B and option D.