An apple is falling from an apple tree next to a lamppost 24 feet tall. When the
ID: 3345048 • Letter: A
Question
An apple is falling from an apple tree next to a lamppost 24 feet tall. When the apple hits the ground, it will be 3.2 feet away from the base of the lamppost. The height of the apple is given by H(t) = 35-12t^2 , where t is seconds after the apple begins to fall. At what rate is the apple's shadow moving along the ground when it is 20 feet above the ground? (Hint: First find the time when the apple is 20 feet above ground, and use that answer to find dh/dt at the moment it is 20 feet above ground)
Please show every step.
Explanation / Answer
At t= 1.118s. the object is 20m. above the ground.
by geometry we can see that
dh/dt = 0.8*dH(t)/dt
at that time dH(t)/dt = -26.83
dh/dt = 0.8*26.83 = 21.47