1. The problem statement, all variables and given/known data A juggler throws a ball straight up into the air with a speed of 10 m/s. With what speed would she need to throw a second ball half a second later, starting from the same position as the first, in order to hit the first ball at the top of the projectory? My problem is I am getting different answers when I use different equations all involving time. Given/Known First Ball: (Vy)i=10 m/s (Vy)f= 0 m/s ay=-9.8 m/s2 Second Ball (Vy)f=0 m/s ay=-9.8 m/s2 2. Relevant equations V = Vo + at Y - Yo = Vot + .5at2 v2 = vo2 + 2a(Y - Yo) Y - Yo = .5(Vo + V)t 3. The attempt at a solution I found the time it takes for the first ball to reach the top of the projectory using equation (V=Vo + at) where V= 0, Vo=10, and a=-9.8. The value I got was 1.02 seconds. I then thought that since the second ball is thrown half a second later, the time for it to reach and hit the top of the projectory should be around .5 seconds. So then I used the same equation: V=Vo + at where V=0, Vo=unknown, a=-9.8, and t=.5 seconds. The value I got was 4.9 m/s. This is wrong. But when I solved for the displacement for the first ball (from initial point to top of projectory) using equation v2 = vo2 + 2a(Y - Yo) where V= 0, Vo=unknown, a=-9.8 the value I got for the displacement was 5.1 m. Now when I plug this value to find the initial velocity of the second ball using equation Y - Yo = Vot + .5at2 where Y-Yo=5.1 m, Vo=unknown, t=.5 seconds (because the second ball is thrown half a second later than the first so since the first one takes around one second the second ball should take around .5 seconds thrown from the same position to hit the first ball), and a= -9.8 the value for initial velocity becomes 12.64 m/s. Why am I getting two different answers using two different equations? Shouldn't both give me the same value of time? This is very frustrating.