Paper Problem Set 4
Due Wed 6 Oct 04

Please write your homework neatly. Don't try to cram all the problems into the minimum space. Show your work clearly, and useful diagrams are always appropriate and may get extra points. You may work with others, but the work should be your own. I expect numeric answers to have a reasonable number of significant figures and proper units.

Note: WebAssign grades only on the answer; I will grade only (mostly) on the method! Make your method clear.

1. A ball is thrown at an angle of 37.0 degrees below the horizontal from a rooftop 25.0 m above the ground. The ball hits the ground a horizontal distance of 13.0 m from where it was thrown. The ball is in ideal free fall from when it leaves my hand until it hits the ground.
(a) Find the time needed for the ball to hit the ground.
(b) Find the initial speed of the ball. (i.e. the magnitude of its velocity.)
(c) Find the components of the ball's velocity just before it hits the ground.


2. A ball is thrown from the ground at a bird perched on a wire. The bird, none too bright, just sits there. The bird is Y = 3.0 m vertically and H = 8.0 m horizontally from the point where the ball is released. You throw the ball with a speed of v₀ = 12 m/s. Determine the angle at which you must throw the ball so as to hit the bird, wake it up, and get it to migrate south where it is warmer! Assume that the ball is in ideal free fall.
[Note: First solve this using symbols, then try putting numbers in. You should end up with an equation that you may not be able to solve easily, but will have to solve numerically or graphically.] Find the numerical answer to 3 significant figures.

Here is an example of such an equation, tan theta = 2 cos theta. Pick an angle and solve left-hand side and the right-hand side. Keep picking angles until the two sides are equal. The table below shows how this was done. The angle is between 51° and 52°. I could continue until I got an answer to any precision I wanted. Some of you may have calculators that will do this automatically. Making graphs is another way to get the solution.

This page maintained by Anne G. Young. Last modified 30-Sep-2004 .