Posted by **Linda** on Monday, April 2, 2012 at 4:18am.

A projectile is fired upward 200 ft from an observer. The height in feet of the projectile after t seconds is given by s=-16t2 + 180t. What is the rate of change of the angle of elevation of the observer to the projectile after 7 seconds?

I don't understand how to get there!

- Math -
**Steve**, Monday, April 2, 2012 at 10:59am
if θ is the angle of elevation,

y = -16t^2 + 180t

tanθ = y/200

sec^2θ dθ/dt = 1/200 dy/dt = 1/200 (-32t + 180)

= -32/200 (t-5)

dθ/dt = -4/25 (t-5) cos^2θ

= -4/25 (t-5) (200^2/(200^2 + y^2)

y(7) = -16*49 + 180*7 = 476

at t=7,

dθ/dt = -4/25 * 2 * 40000/266576 = -.048

Seems kinda small, so you better check the details.

## Answer this Question

## Related Questions

- math - A projectile is fired directly upward with a muzzle velocity of 860 feet ...
- calculus - The height of a projectile launched into the air is given by h (t)= -...
- math - The height of a projectile fired upward is given by the formula s = v0t...
- Intermediate Algebra - If a projectile is fired straight upward from the ground ...
- calculus - A projectile is launched from a platform 20 feet high with an initial...
- Algebra 2 Homework - 1.) Identify the axis of symmetry. f(x) = x2 + 10x + 9 2.) ...
- math - If a projectile is launched from a platform 30 feet high with an initial ...
- College Algebra - A projectile is thrown upward with an initial velocity of 272 ...
- pre-calc - analyzing the motion of a projectile: a projectile is fired from a ...
- algebra - The height in feet of a projectile with an initial velocity of 32 feet...