Question

A golf ball is hit from the ground with an initial speed of 192 feet per second. Assume the starting height of the ball is 0 feet. How long will it take the golf ball to hit the ground?

39 secs
19 secs
12 secs
6 secs

Answer 1

It would be about 12 seconds
:)

Answer 2

The golf ball take 12 seconds to hit the ground.

Thus, option (3) is correct.

Explanation:

We are given,

Initial velocity (u) = 192 feet per second

g be the acceleration due to gravity and its value is 32 feet per second square.

Using Newton's motion of equation

`\text{s}=\text{ut}+(1)/(2)at^2`

Where, s is displacement of body

u is initial velocity of body

a is acceleration of body

t is time

In question, displacement is in term of height so replacing s by h

and acceleration is done due to gravity so replacing a by g

We get,

`\text{h}=\text{ut}+(1)/(2)gt^2`

Since, displacement is changing with time.

`\text{h(t)}=\text{ut}+(1)/(2)gt^2`

Putting values of u and g we get ,

`\text{h(t)}={192t}-(1)/(2)*32t^2`

`\text{h(t)}={192t}-16t^2`

when ball hit the ground height would be 0.

Therefore, h(t) = 0

`{192t}-16t^2=0`

`16t(12-t)=0`

⇒ t = 12 secs

Thus, the golf ball take 12 seconds to hit the ground.

So, option (3) is correct.