# Projectile motion - limited given data

## Homework Statement

Basically, there is a projectile shot from a cannon. When shot, the projectile passes over a net, just barely, which is placed 6.0m away from the cannon, horizontally. The cannon is angled at 40 degrees above the x-axis.

The problem is asking for the muzzle speed of the cannon and how high the net is.

## Homework Equations

delta x = .5(Vf + Vi)t
Vf=at + Vi
delta x = .5at^2 + Vit
Vicos40 = X component Vi
Visin40 = Y component Vi

## The Attempt at a Solution

I know that delta x would be the 6.0m, X component acceleration is 0, and Y component acceleration is -9.8m/s^2. The problem i am running into is working with the limited number of givens here. I know i need to solve for the time it takes to travel to the net(6.0m horizontally). I'm sure it will involve several equations and substitutions to solve for algebraically(we are using non-calc methods in the course), but I'm not sure where to go with this problem.

## Answers and Replies

Kurdt
Staff Emeritus
Science Advisor
Gold Member
I'd solve for muzzle speed first. you have the correct equations for the components of speed. Now you need to set up two equations of motion. The y-component should be set up for speed and the x component for distance. Now you know that at 6m in the x direction the y-component of velocity will be zero. You can rearrange these two equations to find the initial speed. Finding the height of the net from here should be simple.

what you do know is that at some unknown t, just as the ball misses the net,

t=6m/Vo*cos40

and Yo=Vo*sin40-.5at^2. Also tan 40=yo/6. Is that enough to do it?