You're expected to know the "free fall" formula: .A photographer in a helicopter ascending vertically at a constant rate of 12.5 m/s
accidentally drops a camera out the window when the helicopter is 60 m above the ground.
(a) How long will it take the camera to reach the ground?
(b) What will it's speed be when it hits?
. . where: .
We have: .
. . Hence: .
(a) When the camera reaches the ground, its height is 0.
So we have: .
. . a quadratic equation: .
. . which factors: .
. . and has the positive root: .
It takes 5 seconds for the camera to crash to the ground.
(b) The velocity is given by the derivative: .
The speed at impact is 36.5 m/s . . . downward, of course.