# Projectile Motion - Find intial velocity when given an angle?

## Homework Statement

A cannonball is fired with initial speed v0 at an angle 30° above the horizontal from a height of 38.4 m above the ground. The projectile strikes the ground with a speed of 1.3v0. Find v0. (Ignore any effects due to air resistance.)

## Homework Equations

v= Vo + at

v^2 = Vo^2 + 2a(x-Xo)

x = Xo + Vot + .5at^2

## The Attempt at a Solution

I honestly don't know where to start with this problem. I know it needs to be seperated into X and Y components, but it just seems like I don't have enough information to do it.

I mean, what do I know?

x = ?
Xo = 0
Vx = ?
Vox = ? Vcos30 = 1.3Vocos30
Vx = ?
a = 0
t = ?

y = -38.4
Yo = 0
Vy = ?
Voy = ? Vsin30 = 1.3Vosin30
Vy = ?
a = -9.8
t = ?

Can anyone help give me an idea of where to start?

gneill
Mentor
Consider using conservation of energy. You have the initial height and final speed in terms of initial speed. Set up an expression relating initial kinetic energy to final kinetic energy in terms of the speeds given and the change of energy due to the change in height. You should find that the "things you don't know" cancel out of the equation.

This would depend on the angle in which the projectile struck the ground.

gneill
Mentor
This would depend on the angle in which the projectile struck the ground.

What would?

SammyS
Staff Emeritus
Homework Helper
Gold Member
Since all you need to find is the final speed, gneill is right, conservation of energy is the easiest & most direct way to solve the problem.

BTW: Using conservation of energy, you really don't even need the launch angle.

This would depend on the angle in which the projectile struck the ground.

No, I spoke too soon...

lets give you a hint...
1. horizontal velocity would not change
2. since you know the vertical distance you know the height