Problema Solution
A bird sitting 16 feet above the ground in an apple tree dislodges an apple. After how many seconds does the apple land on the ground? (Assume no branches interfere with its fall.)
Answer provided by our tutors
The height of the apple at any time t is
h(t) = 1/2 g t^2 + v_0 t + h_0, where
g = - 32 ft/s^2 is the acceleration due to gravity
v_0 = 0 is the initial velocity (zero here), and
h_0 = 0 is the initial height (16 ft).
When the apple hits the ground its height is zero, so
0 = 1/2 * (-32) t^2 + 16
Divide both sides by 16:
0 = -t^2 + 1
t^2 = 1
t = ±1 sec
But since we're only interested in t > 0:
t = 1 sec
the apple lands on the ground after 1 second.