Question

if there is a 2 kg ball and a 4 kg ball with the same total kinetic energy, then which one will be moving faster?
a the 4 kg ball will be moving faster.
b the 2 kg ball will be moving faster.
c there is not enough information to determine.
d they will both move at the same speed.

Explanation:

Step1: Write the kinetic energy formula

The formula for kinetic energy is \(K = \frac{1}{2}mv^{2}\), where \(K\) is kinetic energy, \(m\) is mass, and \(v\) is velocity.

Step2: Express velocity in terms of kinetic energy and mass

From \(K=\frac{1}{2}mv^{2}\), we can solve for \(v\): \(v = \sqrt{\frac{2K}{m}}\).

Step3: Compare the velocities of the two balls

Let \(K_1 = K_2=K\), \(m_1 = 2\space kg\), and \(m_2 = 4\space kg\).
For the first ball: \(v_1=\sqrt{\frac{2K}{m_1}}=\sqrt{\frac{2K}{2}}=\sqrt{K}\).
For the second ball: \(v_2=\sqrt{\frac{2K}{m_2}}=\sqrt{\frac{2K}{4}}=\sqrt{\frac{K}{2}}\).

Since \(\sqrt{K}>\sqrt{\frac{K}{2}}\) (because if \(a > b>0\), then \(\sqrt{a}>\sqrt{b}\)), the ball with smaller mass (\(2\space kg\)) has a higher velocity.

Answer:

B. The 2 kg ball will be moving faster.