a balloon rises straight up to 5 ft/sec. and a crying child who lost the balloon is standing 40 ft away. how fast does the balloon move away from the child when it is 30 ft above the ground?

Answer 1

If the balloon is at height h, then the distance z from the child to the balloon is

z^2 = h^2 + 40^2
When h=30, z=50

So, now we want dz/dt when h=30

2z dz/dt = 2h dh/dt

Just plug in z=50 and h=30 and dh/dt=5 and solve for dz/dt