Ek 1001 Projectile motion also equation question

[GRod18]

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How far can an animal jump if it can run at 20 m/s and leap from the ground with a vertical velocity of 5 m/s?

Answer: 20 m.

Also I have question regarding the equation V = Sqrt (2gh) EK just seems to say use this equation, but dosen't really explain it for each scenario, so what type if scenario can I use this equation?

For example in for both of these problems, EK said to use the equation.

If a basketball player can jump 2 m into the air, with what vertical velocity does he leave the ground?
An object is dropped from 80 m. with what velocity does it strike the ground?

Why am I using V = sqrt 2 gh for both these problems?

Thanks in advance.

 

[loveoforganic]

1st question) Consider the axis that has changing velocity, i.e. acceleration (this would be the y axis here - acceleration due to gravity. Determine time to reach v naught (this will be where you're at your maximum height). Multiply by two to determine total time of flight. Now use this time to figure out distance moved in the x direction, using the given (and unchanging) v naught in the x direction.

 

[GRod18]

1st question) Consider the axis that has changing velocity, i.e. acceleration (this would be the y axis here - acceleration due to gravity. Determine time to reach v naught (this will be where you're at your maximum height). Multiply by two to determine total time of flight. Now use this time to figure out distance moved in the x direction, using the given (and unchanging) v naught in the x direction.

alright thanks!

 

[Rabolisk]

I don't know exactly how EK introduced that equation, but here is when you use it and how it came about. The equation can be derived from either kinematics or conservation of energy. In cases where gravity is the only vertical force, mgh = 1/2mv^2. If you manipulate that, you get v = sqrt 2gh. Note that h is really change in height, v is change in velocity, and specifically change in vertical velocity. If your object had a horizontal velocity, it would not be affected by gravity, obviously. For those two cases, you were asked to find either initial or final velocity, given change in height. Since the final velocity in the case of the jumping basketball player was 0, and the initial velocity in the case of a dropping ball was 0, this makes the calculation even easier.

Unfortunately, when you are asked to incorporate time (how far one stays in air, one flies, etc.) you have to use the kinematic equations. You need to know three variables to solve for the other two. They are displacement, initial velocity, final velocity, constant acceleration, and time. While mathematically more challenging (if that), you probably understand it more intuitively. After all, I think most college physics classes introduce that before potential and kinetic energies. Sorry If I insulted your intelligence.