when the balloon is at height h,
tanθ = h/300
so,
sec^2θ dθ/dt = 1/300 dh/dt
you know that when h=300, θ=π/4.
You know dh/dt = 80, so just solve for dθ/dt
A hot air ballon lifts off the earth 300m away from an observer and rises straight up at a rate of 80m/min. At what rate is the angle of inclination of the observers line of sight increasing at the time the balloon is 300, above the ground?
1 answer