Hello, Super Mallow!

You are videotaping a race from a stand 123 feet away from the track,

following a car that is moviing at 180 mi/h (264 ft/sec).

How fast will your camera angle theta be changing

(a) when the car is right in fron of you?

(b) a half second later? Code:

B x C
* → → → → → *
| /
| /
123 | /
| /
|θ/
*
A

You are at , 123 feet from the track:

The car is moving to the right from to

. . .and . ft/sec

Let

From right triangle , we have: .

Differentiate with respect to time: .

. . and we have: . .**[1]**

(a) When

Substitute into [1]: .

(b) When

Right triangle ABC has sides and .

. . Its hypotenuse is: .

Hence: .

Substitute into [1]: .

Therefore: .