Hi there, Sorry in advance. This problem is very simple but I can't see where I'm going wrong or what I'm missing. It may even be a numerical mistake, although I have run the numbers a few times. I have a feeling that I'm going to kick myself but anyway... A ball is projected vertically downwards at 4 m/s from the top of a tower 80 m high. Find a) the velocity of the ball as it hits the ground and b) the time it takes to reach the ground. (Taking down to be the positive direction and using g = 9.8) a) use v^2 = u^2 +2as to find v = 12*sqrt(11) m/s or roughly 39.8 m/s (having discarded the negative solution). b) use t = (v-u)/a to find t = (60*sqrt(11) - 20)/49 or approx 3.65 s All fine, all easy. Now, doing the problem again but using s = ut +0.5at^2 I get two solutions for t, one positive (matching the solution above) and a negative solution which may be discarded. All fine still. When I try using s = vt - 0.5at^2 I get two solutions namely t = (60*sqrt(11) - 20)/49 i.e. matching the solution above but my second solution is t = (60*sqrt(11) + 20)/49 or roughly 4.47 s. Why am I coming out with a second positive solution? I'll put my working below in case it's an arithmetic error: s = vt - 0.5at^2 80 = 12*sqrt(11)t - (0.5)(9.8)t^2 4.9t^2 - 12*sqrt(11)t +80 = 0 t = (12*sqrt(11) +/- sqrt((12*sqrt(11))^2 - (4)(4.9)(80)))/9.8 t = (12*sqrt(11) +/- sqrt(16))/9.8 t = (60*sqrt(11) +/- 20)/49 Sorry about this.