lake_effect
New member
- Joined
- Apr 30, 2011
- Messages
- 1
The problem:
The range R of a projectile is
R = [(v^2)/32]*sin(2x)
where v is the initial velocity in feet per second and is the angle of elevation. If v = 2200 feet per second and x changed from 10° to 11°, use differentials to approximate the change in the range.
What I did:
stuck [(2200^2)/32]*sin(2x)into my ti-84, differentiated it at 10, and got the book answer (~4961ft).
However, when I differentiate it with pencil/paper, I get dR = [(2200^2)/32]*2*cos(2x)dx, and when I plug x=10 and dx=1 into that it gives ~284,257, clearly a lot higher than the book answer.
I can't figure out what's causing the inconsistency and it's giving me a headache. Anyone know what's up?
The range R of a projectile is
R = [(v^2)/32]*sin(2x)
where v is the initial velocity in feet per second and is the angle of elevation. If v = 2200 feet per second and x changed from 10° to 11°, use differentials to approximate the change in the range.
What I did:
stuck [(2200^2)/32]*sin(2x)into my ti-84, differentiated it at 10, and got the book answer (~4961ft).
However, when I differentiate it with pencil/paper, I get dR = [(2200^2)/32]*2*cos(2x)dx, and when I plug x=10 and dx=1 into that it gives ~284,257, clearly a lot higher than the book answer.
I can't figure out what's causing the inconsistency and it's giving me a headache. Anyone know what's up?