Question

The largest frog ever found was discovered in Cameroon in 1989. The frog’s mass was nearly 3.9 kg. Suppose this frog is placed on a skateboard with a mass of 2.7 kg. The frog jumps horizontally off the skateboard to the right, and the skateboard rolls freely in the opposite direction with a speed of 2.3 m/s relative to the ground. If the frog and skateboard are initially at rest, what is the horizontal velocity of the frog? Round to the hundredths.

Answer 1

The mass of the frog, m₁=3.9 kg

The mass of the skateboard, m₂=2.7 kg

Let us assume that the right is positive and the left is negative.

Thus the speed of the skateboard, u=-2.3 m/s

The initial momentum of the frog and the skateboard, p=0 kg·m/s²

From the law of conservation of momentum, the total momentum of a system remains constant. That is, the sum of the momentum of the frog and the momentum of the skateboard after the frog jumps should be equal to zero.

Thus,

$m_1v+m_2u=0$

Where v is the horizontal velocity of the frog.

On substituting the known values in the above equation,

$\begin{gathered} 3.9\times v+2.7\times-2.3 \\ \Rightarrow v=\frac{2.7\times2.3}{3.9} \\ =1.59\text{ m/s} \end{gathered}$

Thus the horizontal velocity of the frog is 1.59 m/s