# Throw a Ball: Find Height Above Ground After .7s

• VU2
In summary, we discussed how to calculate the height of a ball above the ground after 0.7 seconds, using the initial position and average velocity. We also explored different approaches to finding the initial velocity and how to apply this information to solve the problem. Overall, it is important to carefully consider the given information and make use of relevant equations in order to find the correct answer.
VU2
Q1) You throw a ball. Assume that the origin is on the ground, with +y-axis pointing upward. Just after the ball leaves your hand its positon is <.06,1.03,0>m. The average velocity of the ball over the next .7s is <17,4,6>m/s. At time .7s after the ball leaves your hand, what is the height of the ball above the ground.

y=1.03+4(.7)-9.8/2×(.7^2)
y=1.429 is my answer, is this correct? I'm using the average velocity as initial, so I'm not sure if I can assume that or not.

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Welcome to PF;
I'm using the average velocity as initial, so I'm not sure if I can assume that or not.
Probably not.
Check it to see if it matters. Depends how accurate your answer needs to be.
You know the acceleration and the average velocity, can you find the y-component of the initial instantaneous velocity.
Note: how is "average velocity" calculated?

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AvgV is calculated by (finalV+initalV)/2=AvgV, can i assume that initial V is 0?

No, you can't assume that. You can, however, calculate the final velocity in terms of the initial velocity, given the acceleration and the time. That will allow you to get the initial velocity from the average.

Oh I see, y-final=y-initial + v(avg)*(t). Therefore, y-final=1.03+4(.7)=3.83?

That will work, too, more directly than what I suggested. I don't know what the notation "<17,4,6>" means, so I don't know if your answer is right.

That is the average velocity vector.

I'm curious now, how would you compute it your way?

VU2 said:
That is the average velocity vector.
That's what I thought, but I was wondering why the z direction was there, since it isn't mentioned in the rest of the problem.

VU2 said:
I'm curious now, how would you compute it your way?
I explained it above. It is essentially the same, except that it takes a roundabout way to get there (basically deriving the equation you used).

Oh I see, thanks!

AvgV is calculated by (finalV+initalV)/2=AvgV, can i assume that initial V is 0?
Average velocity is change in position over change in time:
##\bar{v}=\Delta y/\Delta t = (y_f-y_i)/\Delta t##
... you rearranged that equation to give you the final height given the initial height and the average velocity ... well done.

As an exercise - how would it have been different for the same figures, except the average velocity was timed over 0.1s, but you still want the final height after 0.7s?

Simon Bridge,

Sorry, I was suppose to get back to you sooner. That's an interesting question. I'm not sure how I would approach it, to be honest.

Well - in that case you'd have two time periods ot consider: one short one (with a displacement) to establish the initial velocity and another, longer, one to find the answer. Otherwise the approach is identical to the one you used above.

IRL you often measure the speed of something by timing it over a short distance, and then use that information to work out where the thing will end up.

Simon Bridge,

Yeah that's what I figured too. Thanks for the lesson.

No worries - have fun :D

## 1. How do you calculate the height of a ball after 0.7 seconds?

The height of the ball after 0.7 seconds can be calculated using the formula h = -16t^2 + vt + h0, where h is the height, t is time, v is initial velocity, and h0 is initial height. In this case, we would need to plug in the values for t = 0.7 seconds, v = initial velocity of the ball, and h0 = initial height above ground.

## 2. What is the acceleration due to gravity used in the calculation?

The acceleration due to gravity used in the calculation is typically considered to be 9.8 m/s^2, but this can vary slightly depending on location and altitude. It is important to use the correct value for accuracy in the calculation.

## 3. How do you measure the initial velocity of the ball?

The initial velocity of the ball can be measured using a device called a ballistic pendulum. It involves launching the ball into a pendulum and measuring the height it reaches before swinging back. This can then be used to calculate the initial velocity of the ball.

## 4. Can this calculation be used for any type of ball?

Yes, this calculation can be used for any type of ball as long as the initial velocity and acceleration due to gravity are known. However, the results may not be entirely accurate for balls with significantly different sizes or air resistance factors.

## 5. How is the height above ground related to the time the ball is in the air?

The height above ground is directly related to the square of the time the ball is in the air. This means that the height will increase at a faster rate as time progresses, reaching a maximum height before falling back to the ground.

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