(adsbygoogle = window.adsbygoogle || []).push({}); 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/s^{2}. What is the total mechanical energy at the maximum height of the ball? Answer in units of J.

2. Relevant equations

Mechanical energy = KE + U_{G}+ U_{S}(ignore spring potential energy)

U_{G}= mgh

KE = (1/2)mv^{2}

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 + U_{G}= KE + U_{G}

no U_{G}at launch, and no KE at top of flight in the y-direction -- motion is changing direction -- so

KE in the vertical direction = U_{G}

(1/2)(32 kg)(1360sin44 m/s) = (32 kg)(9.8 m/s^{2})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 + U_{G}in the y-direction

KE = (1/2)(32)(1360cos44)^{2}= 15313200.87 J

U_{G}= (32)(9.8)(45536.98701) = 14280399.13 J

KE^{2}+ U_{G}^{2}= resultant^{2}

resultant = 20938574.93 J

But... that's the wrong answer.

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

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

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