# Homework Help: Work and energy: find the total mechanical energy at the max. height of a projectile.

1. Jan 19, 2010

### therest

1. The problem statement, all variables and given/known data
A 32 kg cannon ball is fired from a cannon with muzzle speed of 1360 m/s at an angle of 44◦ with the horizontal. The acceleration of gravity is 9.8 m/s2 . What is the total mechanical energy at the maximum height of the ball? Answer in units of J.

2. Relevant equations
Mechanical energy = KE + UG + US (ignore spring potential energy)
UG = mgh
KE = (1/2)mv2

3. The attempt at a solution
I actually thought I understood the concepts behind this one fine, but I keep getting the wrong answer.

First I found the height:
Theoretically, mechanical energy is conserved, so E at launch = E at top of flight (w/ max height)
KE + UG = KE + UG
no UG at launch, and no KE at top of flight in the y-direction -- motion is changing direction -- so
KE in the vertical direction = UG
(1/2)(32 kg)(1360sin44 m/s) = (32 kg)(9.8 m/s2)h
h = 45536.98701 m

Then, I attempted to find the mechanical energy at the top of the flight.
Known facts:
* the mass has a vertical acceleration and a horizontal velocity of 1360cos44 m/s
* the mass has both kinetic energy (it is moving) and potential gravitational energy.
* I guessed that the total mechanical energy would be the resultant of these two using the Pythagorean theorem since the two energies are perpendicular to each other.

E at top = KE in the x-direction + UG in the y-direction
KE = (1/2)(32)(1360cos44)2 = 15313200.87 J
UG = (32)(9.8)(45536.98701) = 14280399.13 J

KE2 + UG2 = resultant2
resultant = 20938574.93 J

Do the directions of the vectors not matter? Can someone provide an explanation for this?

2. Jan 20, 2010

### ehild

Re: work and energy: find the total mechanical energy at the max. height of a project

Energy is scalar, has no direction, you simply have to add the different kinds of energy.

"KE2 + UG2 = resultant2" this is wrong.

As for your method, you overcomplicate the calculations. Conservation of the mechanical energy means that the total energy E= KE + PE at the muzzle is the same as at the maximum height.

ehild