How Do You Calculate Takeoff Speed and Fall Time in Physics Problems?

AI Thread Summary
To calculate the takeoff speed of a professional NBA athlete with a vertical leap of 47.3 inches, the initial velocity can be derived using kinematic equations, specifically considering the acceleration due to gravity. For the hot air balloon problem, the camera's descent can be analyzed using the equation for displacement, where the initial velocity is 2.6 m/s and the acceleration is -9.81 m/s² (gravity). The time to reach the ground can be solved by rearranging the displacement equation to isolate time. Understanding that all objects in freefall accelerate at "g" is crucial for both problems. Mastery of these concepts will aid in solving similar physics problems effectively.
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I have 2 problems that I am completely stuck on. I have tried to solve them, but just can't. I am working on summer homework for AP Physics B and I am stuck on these 2.

Homework Statement


The vertical leap of a professional NBA athlete is reported to be 47.3 inches. What is his takeoff speed?

displacement=47.3 inches since it is the leap

Homework Equations


can't find any


The Attempt at a Solution


I do not know what to do. I assume that the takeoff speed is the initial velocity, but I do not know any time values. These time values are needed for any equation I could use to solve this.

Second problem

Homework Statement


A hot air balloon is descending at a rate of 2.6 m/s when a passenger drops a camera.
If the camera is 45 m above the ground when it is dropped, how long does it take for the camera to reach the ground?
displacement= 45m since the camera has to be dropped

Homework Equations


displacement= initial velocity(time)+(1/2)(a)(time^(2))

The Attempt at a Solution


I assume initial velocity is 2.6. And the time is what has to be solved. I can't figure out what acceleration is though.That is what I need to know.
 
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I do not know what to do. I assume that the takeoff speed is the initial velocity, but I do not know any time values. These time values are needed for any equation I could use to solve this.

Have you seen encountered the equation vf^2-vi^2=2ad? If not, you can derive it from vf=vi+at and d= v0*t+(1/2)(a)(t^2). Use the first equation to solve for t, substitute the result into the second, and you should get it after some algebra.

I assume initial velocity is 2.6. And the time is what has to be solved. I can't figure out what acceleration is though.That is what I need to know.

All objects in freefall accelerate at "g". (Incidentally, this probably comes close to being the first physics law ever discovered. It predates Newton by several decades.)
 
For #1 then, what is the acceleration. And what would vf be.
 
ama said:
For #1 then, what is the acceleration. And what would vf be.

What did ideasrule say about objects in freefall?

What do you suppose his velocity is when he's at his highest distance from the ground?
 
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