Vertical Kinematics: Solving for Jump Time

[sprinter08]

Homework Statement

A kangaroo jumps to a vertical height of 2.8m. How long was it in the air before returning to Earth?

Homework Equations

delta y= Vot + 1/2at^2

The Attempt at a Solution

I had to get t by itself so I rearranged the equation to say: t= delta y/.5(9.8) all under a square root. First off, I'm not sure if I set up the equation correctly, and secondly, I am not sure if just the top (delta y) goes under the square root or both the top and bottom(or the whole side of the equation) goes under the square root.

 

[Doc Al]

Not sure of your approach here. What's Vo?

Try this: Start at the top. Figure out how long it takes for the kangaroo to fall a distance of 2.8m. What would Vo be in that case? How would that time relate to the total time the kangaroo was in the air?

 

[sprinter08]

Vo in this case would be zero, I believe...and if it would be zero, then it would eliminate the first part of the equation (Vot).

 

[sprinter08]

Oh, sorry, I misread your question I think. I'm not sure if I know how to figure that out.

 

[tiny-tim]

I had to get t by itself so I rearranged the equation to say: t= delta y/.5(9.8) all under a square root.
First off, I'm not sure if I set up the equation correctly, and secondly, I am not sure if just the top (delta y) goes under the square root or both the top and bottom(or the whole side of the equation) goes under the square root.

Looks ok to me

Vo = 0, and y = (1/2)at^2, so t^2 = 2y/a, so t = ± √(2y/a).

You seem to have the technique right - why are you unsure?

 

[sprinter08]

well, I was just wondering if I were to take the square of the top and then divide it by the bottom, or if I divided the top by the bottom and then took the square root. I divided the top by the bottom, and then took the square root to get .57. But then I think I would need to multiply it by 2 to get 1.14 seconds. I'm not exactly sure.

 

[Doc Al]

Vo in this case would be zero, I believe...and if it would be zero, then it would eliminate the first part of the equation (Vot).

That's right.

Oh, sorry, I misread your question I think. I'm not sure if I know how to figure that out.

Sure you do. That's exactly what you're doing! (I don't see any Vot in your final equation.)

well, I was just wondering if I were to take the square of the top and then divide it by the bottom, or if I divided the top by the bottom and then took the square root. I divided the top by the bottom, and then took the square root to get .57. But then I think I would need to multiply it by 2 to get 1.14 seconds. I'm not exactly sure.

You divide first, then take the square root--just like you did. And the reason you need to multiply by two, is that you only solved for the time it takes to fall from the highest point (or reach the highest point). That's only half of the total time.

 

[sprinter08]

Thank you!