Answer:
4.75 seconds
Step-by-step explanation:
Initial height of the ball from the ground = 10 feet
Upward initial velocity given = 55 feet per second
Value of g ( acceleration due to gravity) = 32.2 feet per s²
Motion of the ball:
The ball first goes vertically upwards, gravity decelerates the body and it momentarily comes to rest at a point in its upward trajectory, which is the point of maximum height. From this point, to the ground, the ball behaves as a freely dropped body.
Till the ball reaches its maximum height:
u = + 55
v = 0 ( final velocity is zero)
a = - 32.2 (since it is deceleration)
we know that <em>v = u + at </em>
⇒ 0 = 55 - 32.2t
⇒ t = 1.7 s
Also , we have <em>s = ut + (1/2)at²</em>
Here, s is the maximum height from the point where ball is thrown
So, s = 55(1.7) - (0.5)(32.2)(1.7)(1.7)
⇒ s = 140 feet
So at a height of 140 feet + 10 feet (initial height) = 150 feet, the ball acts as a freely dropped body.
Here, u = 0
a = +32.2
s= 150
<em>s = ut + (1/2)at²</em>
⇒ 150 = 0.5 ( 32.2) (t²)
⇒ t² = 300/32.2 = 9.31
⇒ t = 3.05 sec
So total time = 1.7 + 3.05 = 4.75 seconds
