Question

A monkey of mass $20kg$ rides on a $40kg$ trolley moving at a constant speed of $8m/s$ along a horizontal track. Frictional force can be neglected. If the monkey jumps vertically, with respect to the moving trolley, the catch the overhanging branch of a tree, the speed of the trolley after the monkey has jumped off is:-

Answer 1

Step 1: Given data.

1. The mass of the monkey is $20kg$.
2. The mass of the trolley is $40kg$.
3. The initial speed of the system monkey and trolley is $8m/s$.

Step 2: Concept and formula to be used.

1. According to the law of conservation of momentum, the momentum of an isolated system remains the same.
2. The formula of momentum $p$ is $p=mv$. where $m$ is the mass of the system and $v$ is the velocity of the system.

Step 3: Find the speed of the trolley after the monkey has jumped off.

Find the initial momentum of the given system.

Initially, A monkey of mass $20kg$ rides on a $40kg$ and the velocity of the trolley is $8m/s$ along a horizontal track.

So, the initial momentum $p_1$ is given by: $p_1=(20+40)8$.

Assume that, the velocity of the trolley when the monkey jumps vertically with respect to the moving trolley and catches the overhanging branch of a tree is $v$.

And final momentum $p_2$ when the monkey jumps vertically, with respect to the moving trolley and catches the overhanging branch of a tree is given by: $p_2=40v$.

So, according to the law of conservation of momentum.

$$\begin{gathered} p_1=p_2 \\ \Rightarrow 480=40v \\ \Rightarrow v=\frac{480}{40} \\ \Rightarrow v=12 \end{gathered}$$

Therefore, the speed of the trolley after the monkey has jumped off is $12m/s$.