Homework SourseA camera is set up at the starting line of a drag race 80 fe
A camera is set up at the starting line of a drag race, 80 feet from a dragster at the starting line. Two seconds after the start of the race, the dragster has traveled 240 feet and the camera is turning .75 rad/s while filming the dragster. What is the speed of the dragster at this point?
Solution
Express the distance the dragster has traveled, d, as a function of x, the angle of the camera.
tan (x) = d/80
d = 80 tan(x)
We can figure out x at the point in time where d has traveled 240 ft.
tan (x) = 240/80 = 3
x = arctan(3) = 1.249 rad
Take the derivative of our function for d with respect to time
dd/dt = 80 * sec^2 (x) * dx/dt
Plug in known values
dd/dt = 80 * sec^2(1.249) * 0.75
dd/dt = 600 ft/s
