https://file.aiquickdraw.com/mathbot/file/1726421708843773z23hz.jpg

Let's go through each of the problems in the image.

### Problem 10:
Two particles of mass \(m\) and \(3m\) are moving with the same speed \(v\) in a vacuum at right angles. The particle of mass \(m\) is moving in the x-direction, while the particle of mass \(3m\) is moving in the negative y-direction. A force \(F\) acts on the particle of mass \(m\) for a duration \(T\), which causes its velocity to become \(4v\) in the original direction. The same force \(F\) acts on the particle of mass \(3m\) for the same time. Find the new velocity \(\vec{v}'\) of the particle with mass \(3m\).

- We are given a multiple-choice set of answers to choose from.

### Problem 11:
A tennis ball of mass \(m\) is held above a basketball of mass \(M = 11m\). Both balls are released from rest and fall through a distance \(h\). The basketball elastically collides with the ground and then collides elastically with the tennis ball. The problem asks us to find the height to which the tennis ball will rebound after this collision.

- This involves momentum conservation and energy conservation principles for elastic collisions.

### Problem 12:
A small disk of mass \(m\) rests on the horizontal surface of object \(A\), which has mass \(M = 2m\). The disk is set into motion in the horizontal direction with velocity \(v\), and the question asks for the maximum height the disk will rise to after leaving the surface of object \(A\), assuming the surface is smooth.

- The multiple-choice answers involve terms of \(v^2\) and \(g\).

I can now help you solve these problems. Which problem would you like to start with?

Analyze the velocity of two particles moving at right angles, find the rebound height of a tennis ball after an elastic collision, and determine the maximum height reached by a disk after it is set in motion.

This page explores three physics problems involving elastic collisions and the conservation of momentum. Topics include the motion of particles in vacuum, the rebound height of a tennis ball after colliding with a basketball, and the maximum height a disk reaches after breaking off from a smooth surface.

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