Question

This is a calc II problem that i just can't figure out.

In a free-fall experiment, an object is dropped from a height of 256 ft. A camera on the ground 500 ft from the point of impact records the fall of the object.

a)find the position function that yields the height of the object at time t assuming the object is released at t=0. At what time will the object reach ground level?

b) Find the rates of change of the angle of elevation of the camera when t=1 and 2.

Answer 1

A position function it just going to be:
\[h = h_0-\frac{1}{2}g t^2 \Rightarrow h = 256 - \frac{1}{2}(32.174)t^2\]
h_0 is initial height. g is gravity in ft/sec^2 since the units we are working with are ft. To figure out what time the object hits the ground, set this equation = 0 and solve for t

Answer 2

For second question, you need to draw the right triangle with the path of the object falling as one side (a leg), and the 500 ft as the other leg. The angle is going to be with the camera. Use the trig function tan to get a formula that relates the height of the falling object to the angle.

Answer 3

thank you. the back of my book just tell me the answer. they don't explain how to get that answer

Answer 4

for the second one do I need to take the derivitive? since it's a rate of change?

Answer 5

Right :)