[Physics] Vertical motion initial velocity given max height

homework-and-exerciseskinematicsprojectile

I'm having a hard time finding a formula that calculates the initial vertical velocity for a projectile that should reach a certain height.

I'm using this formula to calculate both vertical and horizontal displacement:

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This works great if I have the initial velocity, with any angle (even for motion in vertical axis only!).

Problem is that I have maximum height and angle, and I need to calculate that initial velocity. I tried the following formula:

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And it works for angles other than 90 degrees (PI / 2). But I need to handle the case of vertical motion only. This angle works in the previous formula, but not here. Also obvously, I need to handle the other angles too (for which case this formula works good).

Is there any other formula I can try?

I have tried Wikipedia and Khan Academy, but couldn't find what I needed.

Best Answer

Thanks to John Rennie and Goodies, I have reached the following equation:

$$v_{0} = \sqrt{2gh}$$

This works fine in my case, and calculates the initial velocity for a projectile fired upwards at a 90 degree angle, which should reach a certain height.

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