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

t = 3.25 seconds.

Step-by-step 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=(-50 \pm √(50^2-4* (-16)(7)) )/(2(-16))\\\\t=(-50 + √(50^2-4* (-16)(7)) )/(2(-16)), (-50- √(50^2-4* (-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.