(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

At what height h above the ground does the projectile have a speed of 0.5v?

2. Relevant equations

K_1 + U_1 = K_2 + U_2

K = 1/2mv^2

U = mgh

3. The attempt at a solution

I made the point where the speed is .5v = point 1, and the maximum height = point 2.

Point 1:

K_1 = 1/2m(v_1x^2 + v_1y^2)

U_1 = mgh

Point 2:

K_2 = 1/2m(v_2x^2 + v_2y^2)

U_2 = mg(v^2/2g) = (mv^2)/2 <--maximum height, I got this from the previous part.

Then it's just plug and chug into the eqn K_1 + U_1 = K_2 + U_2 but I came out with the wrong answer which is (-v^2/8g). Oh I took out the v_1x^2 and the v_2x^2 because the x component remains constant throughout and I also took v_2y^2 because it's 0 at maximum height.

I must have done something wrong somewhere but I have no idea (probably my setup) so pls help?

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# Basic Kinetics

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