Step-by-step explanation:
Set the origin of the coordinate system at the top of the tower.
Given:
y = -234 ft (when the ball hits the ground)
v0 = +19ft/a
g = 32 ft/s^2
a) The equation of motion. for this freely-falling body is
y = v0t - (1/2)gt^2
When the ball hits the ground, t = T (time of flight)
----> -234 ft = (19 ft/s)T - (1/2)(32 ft/s^2)T^2
Rearranging the terms and dropping the units momentarily for brevity, we get
(16)T^2 - 19T - 234 = 0
This is a quadratic equation whose solution is
T = (1/32)[19 +- {(-19)^2 - 4(16)(-234)}]^(1/2)
= 4.46 s. or -2.68 s
Therefore, the time of flight T = 4.46 s
b) To find the velocity upon impact, we use
v = v0 - gt, where t = T = 4.46 s
= (19 ft/s) - (32 ft/s^2)(4.46 s)
= -123.7 ft/s
The negative sign means that its velocity is pointing down.
