# Homework Set 1

Note: Some of the problems have hints in Mastering Physics which will guide you through the problem tutorial style. There is NO penalty for using the hints! You have unlimited attempts at a question and will not lose any credit for entering wrong answers before getting the right one.

## Motion of two rockets

This is a similar kind of image to the one we generated from the falling weight video. There is an equal time interval between each appearance of the moving objects and we can use the change in position between successive appearance to infer something about the motion.

## Problem 2.61

This is a free fall problem, so you know what the acceleration $a$ is. You can use one of the equations of motion to find out what the velocity is at the top of the window. You can then use another one of the equations to work out the distance required to achieve that velocity when the object falls from rest. The key is to look at the equations for each step and decide which one is the best to help you get from what you know to what you want to know.

$\large v=\int^{t}_0 a\,dt = v_{0}+at$

$\large x=\int^{t}_{0} v\,dt = x_{0}+v_{0}t+\frac{1}{2}at^2$

$\large v^{2}=v_{0}^2+2a(x-x_{0})$

## Problem 2.74

Another free fall problem. You know the initial height and velocity and the acceleration and you want to know the height at a given time before the pelican hits the water. To know where the pelican is at a given time before it hits the water you're going to have to first work out when that is with respect to the initial time.

## Motion Diagram and Gravity Graphing Question

This question requires to apply our equations of motion at several points through a trajectory and place them on a graph. See if you can do this problem without a calculator (it's not too hard as in this question $g=10ms^{-2}$)

## Rocket Height

Break this motion up in to two parts. Make sure to get all your signs right when you take the information you work out for the first part in to the second part. This problem has hints in Mastering Physics to help guide you to the solution.

## Problem 3.13

First convert each of the vectors so that they are expressed in unit vector form (use trigonometry). Then the remaining operations are just a matter of working out each component of the resultant vector.

Enter your answer in the form $a\hat{i}+b\hat{j}$

## A canoe on a river

First convert the velocity of the canoe in to components along the direction of the river and perpendicular to it. This makes it a lot easier to subtract of the velocity of the river to find the velocity of the canoe relative to the river. This problem has hints in Mastering Physics.

## Problem 3.70

A fairly typical relative velocity problem.

## Problem 3.78

An algebraic relative velocity problem.

## Problem 3.88

Use the equations of motion for a cannon from lecture 3. You need to use the known position at a particular time to work backwards and find out what the initial velocity and angle were.

## Problem 3.56

Take a look a the approach used to find the motion path in Lecture 3. Instead of solving for y=0 solve for y=h. Note that the problem only wants you to find the solution for h>0. Also note that Mastering Physics requires that you type trig functions with brackets, e.g $\sin(\theta)$ not $\sin\theta$.

To get you started:

You want to solve the following equation for x

$h=x\frac{\sin\theta_{0}}{\cos\theta_{0}}-\frac{g}{(2v_{0}^{2}\cos^2\theta_{0})}x^2$

Rearranged in to standard quadratic form this is:

$x^2-\frac{2v_{0}^{2}}{g}\sin\theta_{0}\cos\theta_{0} x+h\frac{(2v_{0}^{2}\cos^2\theta_{0})}{g}=0$

Only one of the solutions for x is positive if $h>0$ and this is the one you're looking for.

## Delivering a package by air

Projectile motion with zero degree launch angle and a known initial horizontal velocity. You'll need to do some unit conversion in this problem! This problem has hints in Mastering Physics. 