Question

A person throws a baseball from height of 7 feet with an initial vertical velocity of 50 feet per second. Use the vertical motion model, h = -16t2 + v … t +s, where y is the initial velocity in feet per second and s is the height in feet, to calculate the amount of time the baseball is in the air before it hits the ground.

Answer 1

Answer:

t = 3.25 seconds.

Explanation:

A person throws a baseball from a height of 7 feet with an initial vertical velocity of 50 feet per second is given by :

$h=-16t^2+vt+h_0$

$h=-16t^2+50t+7$

We need to find the amount of time the baseball is in the air before it hits the ground. ATQ,

h = 0

$-16t^2+50t+7=0\\\\t=\dfrac{-50 \pm \sqrt{50^2-4\times (-16)(7)} }{2(-16)}\\\\t=\dfrac{-50 + \sqrt{50^2-4\times (-16)(7)} }{2(-16)}, \dfrac{-50- \sqrt{50^2-4\times (-16)(7)} }{2(-16)}\\\\t=-0.134\ s,3.25\ s$

Neglecting negative value, t = 3.25 s

So, the baseball will hit the ground at t = 3.25 seconds.