Kinematics problem

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1. Sep 3, 2016

AStupidHippo

1. The problem statement, all variables and given/known data
While standing at the edge of the roof of a building, you throw a stone upward with an initial speed of 6.91 m/s. The stone subsequently falls to the ground, which is 16.5 m below the point where the stone leaves your hand. At what speed does the stone impact the ground? How much time is the stone in the air? Ignore air resistance and take g = 9.81 m/s2.

I solved for impact velocity fairly easily. v=19.2 m/s

I'm having trouble with finding time. I have to use an online HW submitter (Sapling Learning), but it keeps saying I'm wrong.

2. Relevant equations
v^2 = u^2 +2as
v=u+at
3. The attempt at a solution

19.2 = 6.91 + 9.81(t)
12.29=9.81(t)
t=1.25 seconds
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2. Sep 3, 2016

Hans Herland

Greetings.

Could you show how you come up with t = 1.25s?

I tried the problem myself, and I do get a different answer, using your formula: v = v0 + at
You have to make the formula be based on t instead, which gives you: t = (v - v0) / a

Now I did the calculation twice: once for figuring out the air-time the stone uses to the top of the upward throw, and one for calculating the amount of time the stone takes from the top of the throw all the way to the bottom.

The first calculation has v0 = 6.91
The second calculation has v0 = 0

In the first calculation, a will be negative (assuming we've set a positive direction upwards)
In the second calculation, a will be positive.

This gives you two numbers you should be able to add together to see the total amount of air time. There's probably a better method of doing this in one calculation.

3. Sep 3, 2016

AStupidHippo

Hi!

So this is what I did: (Impact velocity - initial velocity)/a = t
(19.2-6.91)/9.81=t
This gave me t=1.25

4. Sep 3, 2016

Hans Herland

This should give you the time it would take for the stone to drop if it was thrown directly towards the ground. Since the stone is thrown upwards, you'll need to find the time it takes for the stone to travel with initial velocity of 6.91, to impact velocity of 0 (where the stone starts dropping).

5. Sep 3, 2016

AStupidHippo

Ok. So I should make v= 0 and solve for time with this: 0=6.91-9.81t
t=.7
And then I add it it to 1.25? So the answer is 1.25+.7= 1.95

6. Sep 3, 2016

Hans Herland

You should re-check the 1.25 number, since that's still based on the time it would have taken for the stone to drop at the height it was thrown in. Remember that it now drops from a higher altitude, making the drop longer than before, and the initial velocity of the drop is 0.

Since the stone was thrown up into the air, it accelerated downwards due to gravity, making it slow down and eventually "stop". When this happens, the stones velocity starts accelerating again, but this time the velocity also points downwards.

I got 0.7 seconds as well when calculating the time it takes for the stone to reach the top of the throw.

7. Sep 3, 2016

AStupidHippo

Yes. It's 1.25+.7+.7=2.6. This is the correct answer. Thank you!

8. Sep 3, 2016

LogarithmLuke

Alternatively you could use the v=vo +at formula, but have v0 be negative, because at the bottom you are moving the oppositve way of the intitial throw. If you have movement in two different different directions one of the values has to be negative.

9. Sep 3, 2016

haruspex

Indeed, this is the correct way to solve the problem. Since acceleration is constant throughout, it is quite unnecessary to break it into separate upward and downward stages.