It takes 2 seconds long to hit the ground. The correct answer between all the choices given is the second choice. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.
Answer:
Option 2nd is correct
2 seconds does it take to hit the ground
Step-by-step explanation:
The equation of projection is given by:
[tex]s(t) = -at^2+v_ot+h[/tex]
where,
[tex]a \approx -16 m/s^2[/tex]
[tex]v_0[/tex] is the initial velocity
and h is the initial height.
As per the statement:
A ball is dropped from a treetop 64 feet above the ground.
Initial height: s(0) = 64 feet
Since, initial velocity [tex]v_0 = 0[/tex]
then equation becomes:
[tex]s(t) =-16t^2+0t+64[/tex]
To find the how long does it take to hit the ground.
Substitute s(t) = 0 then ;
[tex]0 =-16t^2+0t+64[/tex]
⇒[tex]0 = -16t^2+64[/tex]
⇒[tex]16t^2= 64[/tex]
Divide both sides by 16 we have;
[tex]t^2 = 4[/tex]
Simplify:
[tex]t =\pm \sqrt{4} =\pm 2[/tex]
Since, t is the time cannot be in negative
⇒t = 2 seconds
Therefore, 2 seconds does it take to hit the ground.
