K = 1/2mv^2
U = mgh
At what height h above the ground does the projectile have a speed of .5v?
Express your answer in terms of v and the magnitude of the acceleration of gravity g .
3 Answers

K = U
0.5mv^2 = mgh
0.5v^2 = gh
h = (0.5v^2)/g
Since the speed is 0.5 v:
h = [0.5 (0.5v)^2]/g
h = (0.125v^2)/g
h = v^2 / 8g

3v^2/8g

gh_2= 1/2(V_1^2V_2^2)
h=(V_1^2V_2^2)/2g= [V_1^2(0.5V)^2]/2g
=(V_1^20.25V_1^2)/2g = (0.75V_1^2)/2g =3V^2/8g