A balloon rises at a rate of 4 meters per second from a point on the ground from an observer. Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 50 meters above the ground.
Asked By Ana On 01/30/2017 00:00
dx/dt = 4 m/s
tantheta = x/50 = d/dt(tantheta) = d/dt(x/50)
sec^2 theta * dtheta/dt = (1/50) * (dx/dt) = dtheta/dt = cos^2 theta/50 * (dx/dt)
tantheta = 50/50 = 1 = theta = 45 degrees
dtheta/dt = cos^2(45 degrees)/(50) * (4 rad/sec) = (((sqrt(2)/(2))^2)/50 * (4 rad/sec) = 1/25 rad/sec
the rate of change is 1/25 rad/sec
Answered On 02/01/2017 00:58
i think there is a missing information here, the horizontal distance of the observer to the balloon.
Answered On 02/16/2017 05:15