Question

I have a physics problem that gives me a projectile launched. It tells me the angle...

I have a physics problem that gives me a projectile launched. It tells me the angle above horizontal, the MINIMUM speed while in flight, and the amount of meters the ball traveled when it lands. The question asks for max height. What's tripping me up is this MINIMUM velocity. Where on the projectile is the velocity a minimum. I was thinking the minimum velocity would be at the highest point, because at the highest point the velocity is 0, however, this problem gives me a minimum velocity that is not 0. I'm just confused on what equation(s) I should be using to find the ball's max height given these three numbers (an angle, a min velocity, and a distance traveled). *Ignore air resistance

You are right that minimum velocity is zero at the top of projectile motion but but wait .....we are talking about projectile motion. There are always two components of velocity.

vx ( horizontal component) and vy ( vertical component)

At the top of projectile motion , only vy = 0 , but vx has some value . Therefore at the top, we have minimum velocity

In case of no air resistance, the horizontal component of velocity ( vx ) will remain the same everywhere.

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distance traveled, x = vx t

x = v cos * t

at maximum height, vy = 0, so we have this equation

y = vyt - 1/2gt2

ymax = 0 - 1/2 * g * ( x / v cos)2

ymax = 1/2 * g * ( x / v cos)2