# Homework Help: Calc III differential

1. Feb 24, 2014

### reddawg

1. The problem statement, all variables and given/known data
The range of a projectile fired (in a vacuum) with initial velocity V0 and inclination angle θ from the horizontal is R = (1/32) * (V0)2 * sin(2θ).

Use differentials to approximate the change in range if V0 is increased from 400 ft/s to 410 ft/s and θ is increased from 30° to 31°.

2. Relevant equations
Setting up my equation:

dR = (∂R/∂V0) * dV0 + (∂R/∂θ) * dθ

3. The attempt at a solution
Taking the partials and substituting values:

sin(60°)/250 + cos(60°)/10,000 = 5216.51 ft.

This answer seems unreasonable, can anyone check my work?

2. Feb 24, 2014

### SteamKing

Staff Emeritus
It's not clear what you have done since you don't show all the steps in taking your differentials.

Did you apply all of the derivative rules correctly? I can't tell from the attempt at your solution, since you have already substituted numbers. What happened to the factor (1/32) from the original range equation?

3. Feb 24, 2014

### reddawg

The attempt at a solution:

Taking the partials:

∂R/∂V0 = (sin(2θ)*V0)/16

∂R/∂θ = (cos(2θ)*(V0)2)/16

dV0 = 10

dθ = 1

I then substituting and simplified.

4. Feb 24, 2014

### SteamKing

Staff Emeritus
Did you use radian measure for your dθ?

5. Feb 24, 2014

### reddawg

I thought I had calculator in degree mode, however I went back through with radian and verified d(theta) was in radians.

Also there was a sign error in my calculations so the new answer is 129.24 ft which seems more reasonable don't you think?

6. Feb 24, 2014

### SteamKing

Staff Emeritus
Yes.

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