Answer:
The golf ball take 12 seconds to hit the ground.
Thus, option (3) is correct.
Step-by-step 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
[tex]\text{s}=\text{ut}+\frac{1}{2}at^2[/tex]
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,
[tex]\text{h}=\text{ut}+\frac{1}{2}gt^2[/tex]
Since, displacement is changing with time.
[tex]\text{h(t)}=\text{ut}+\frac{1}{2}gt^2[/tex]
Putting values of u and g we get ,
[tex]\text{h(t)}={192t}-\frac{1}{2}\times32t^2[/tex]
[tex]\text{h(t)}={192t}-16t^2[/tex]
when ball hit the ground height would be 0.
Therefore, h(t) = 0
[tex]{192t}-16t^2=0[/tex]
[tex]16t(12-t)=0[/tex]
⇒ t = 12 secs
Thus, the golf ball take 12 seconds to hit the ground.
So, option (3) is correct.
