A man of mass 60 kg standing on a platform of mass 30 kg jumps horizontally with an acceleration 6 m/s^2 . Find acceleration of the platform.

To solve this problem, we can apply Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. When the man jumps off the platform, he exerts a force on the platform, and in turn, the platform exerts an equal and opposite force on him. This interaction will cause the platform to accelerate in the opposite direction to the man's jump.

Understanding the Forces Involved

First, let’s identify the forces at play. The man has a mass of 60 kg and he jumps with an acceleration of 6 m/s². The platform has a mass of 30 kg. When the man jumps, he pushes against the platform, which results in the platform moving in the opposite direction.

Calculating the Force Exerted by the Man

We can calculate the force exerted by the man during his jump using Newton's second law, which states that force equals mass times acceleration (F = m × a).

• Mass of the man (m) = 60 kg
• Acceleration of the man (a) = 6 m/s²

Now, substituting the values into the formula:

Force exerted by the man (F) = 60 kg × 6 m/s² = 360 N

Applying Newton's Third Law

According to Newton's third law, the platform experiences an equal and opposite force of 360 N in the opposite direction. Now, we need to find the acceleration of the platform caused by this force.

Calculating the Acceleration of the Platform

We can again use Newton's second law for the platform:

• Mass of the platform (M) = 30 kg
• Force acting on the platform (F) = 360 N

Using the formula F = M × a, we can rearrange it to find the acceleration (a) of the platform:

a = F / M

Substituting the values:

a = 360 N / 30 kg = 12 m/s²

Final Result

The acceleration of the platform is 12 m/s² in the direction opposite to the man's jump. This example illustrates how the principles of physics, particularly Newton's laws, help us understand the interactions between objects in motion.