9.5 Collisions in Multiple Dimensions

Suppose the initial velocities were not at right angles to each other. How would this change both the physical result and the mathematical analysis of the collision?

Notice that the mass of the air in the tank was neglected in the analysis and solution. How would the solution method changed if the air was included? How large a difference do you think it would make in the final answer?

Momentum for a system can be conserved in one direction while not being conserved in another. What is the angle between the directions? Give an example.

A 200-kg rocket in deep space moves with a velocity of $\left(121 \text{m}/\text{s}\right) \hat{i} + \left(38.0 \text{m}/\text{s}\right) \hat{j}$. Suddenly, it explodes into three pieces, with the first (78 kg) moving at $− \left(321 \text{m}/\text{s}\right) \hat{i} + \left(228 \text{m}/\text{s}\right) \hat{j}$ and the second (56 kg) moving at $\left(16.0 \text{m}/\text{s}\right) \hat{i} - \left(88.0 \text{m}/\text{s}\right) \hat{j}$. Find the velocity of the third piece.

Three 70-kg deer are standing on a flat 200-kg rock that is on an ice-covered pond. A gunshot goes off and the deer scatter, with deer A running at $\left(15 \text{m}/\text{s}\right) \hat{i} + \left(5.0 \text{m}/\text{s}\right) \hat{j}$, deer B running at $\left(−12 \text{m}/\text{s}\right) \hat{i} + \left(8.0 \text{m}/\text{s}\right) \hat{j}$, and deer C running at $\left(1.2 \text{m}/\text{s}\right) \hat{i} - \left(18.0 \text{m}/\text{s}\right) \hat{j}$. What is the velocity of the rock on which they were standing?

An oxygen atom (mass 16 u) moving at 733 m/s at 15.0° with respect to the $\hat{i}$ direction collides and sticks to an oxygen molecule (mass 32 u) moving at 528 m/s at 128° with respect to the $\hat{i}$ direction. The two stick together to form ozone. What is the final velocity of the ozone molecule?