A ball is launched vertically up from the ground, how long does it stay in the air?

helpme2012

1. The problem statement, all variables and given/known data
A ball is launched vertically up from the ground. The initial speed of the ball is 37.5m/s. How long does it stay in the air?


2. Relevant equations
The 5 kinematic equations


3. The attempt at a solution
I figured the final speed would be 0m/s, and used the formula vf=vi+a*t so 0=37.5+(-9.8)t
and got t=3.83s... I don't think that's right, and was wondering if someone could please help me out? Any help is appreciated. Thanks

PhanthomJay

Welcome to PF! The speed of the ball is 0 when it reaches the top of its trajectory, so the time you have calculated is the time it takes to reach the top of its path. What do you suppose is the time it takes to come back down to the ground?

helpme2012

Thanks for the reply, I appreciate being welcomed here. I'm really confused, I'm sorry but I honestly have no idea. I was thinking it would be another 3.83s to come back down but that can't be right..

PhanthomJay

And why not?

helpme2012

I'm just doubting myself right now haha, according to the book it's worth 4 marks so I figured maybe I was missing something.

Fifty

A ball is launched vertically up from the ground. The initial speed of the ball is 37.5m/s. How long does it stay in the air?

If you're stuck on a question, just always state the given even if you have no idea what to do!

Given: a = -9.81ms_-2 (I prefer to write it like this on one line, one ms_-2 is equal to a m/s/s or a m/s²

v_i = 37.5ms_-1

d = ?

v_f = 0 (at the top of its trajectory, the ball stops momentarily, then comes back down)

v_f² = v_i² + 2ad

Find the displacement, and then you can use a different equation to solve for time. (You now have four variables. Before, the three variables you had in your given restricted you to the use of the only equation that does not have time. Solving for displacement opens up the possibility to more equations, four of which include time)
I had a feeling I just undermined what phantom said, so attempt the question again before you look at the spoiler please :)

PhanthomJay

Try using one of the other kinematic equations, the one with displacement as a function of initial velocity, time and acceleration. The initial velocity and the acceleration of gravity are known, and what it is the value of the displacement between its initial position when it is thrown from the ground and its final position when it comes back down to the ground? Solve for t.....

helpme2012

Hey guys, I found the displacement to be 71.75m. I used the equation suggested by Fifty and did this:
d = vft - 1/2at2
71.75 = 0t - 1/2(-9.8)t2
71.75 = 4.9t2

I divided 4.92 from both sides so after I had this:

14.64 = t2

I took the square root of 14.64 and got 3.826s, rounded off to 3.83s

What do you guy think? Did I make any mistakes?

PhanthomJay

It depends upon what your final answer is for the total time of the flight from start to finish. Incidentally, watch your signs...if displacement is positive down, then acceleration of gravity is positive down...

helpme2012

7.66 seconds for the total flight from start to finish?

PhanthomJay

Yes!