# A difficult projectile problem

1. Feb 7, 2012

### jysim

1. The problem statement, all variables and given/known data
A cannon is fired at an angle of 30 degrees above the horizontal from a cliff that is 20m above a flat river bottom. What is the initial speed of the projectile if it is found to land 40m from the base of the cliff?

Please provide me with relevant explainations as well. Thanks! :D

2. Feb 7, 2012

### sjb-2812

Resolve the speed into horizontal and vertical components.

3. Feb 7, 2012

### jysim

The speed is not provided in the question.

4. Feb 7, 2012

### sjb-2812

Call the speed v, then.

5. Feb 7, 2012

### sjb-2812

To clarify, assuming I've set this up right, if you do this ultimately you end up with two equations in v and t, which you can solve for either.

6. Feb 8, 2012

### jysim

What I got so far was Vi cos 30t = 40
Is the total vertical distance merely 20m since the vertical displacement of the cannonball during the parabolic trajectory is 0? (Since it goes up and down the same distance?) - pardon my bad english lol!

Is the "t" in the Vi cos 30t = 40 equation the total time taken for the entire projectile motion or just the upper symmetrical part of the projectile (excluding the 20m descent)?
Thanks!

7. Feb 8, 2012

### sjb-2812

First part yes (don't forget to check your signs), and for the second part t is the total time (as you'd using the total time for both the horizontal and vertical components, no?)