A ball is thrown vertically upward from the ground with a velocity of 30m/s. (a) how
long will it take to rise to the highest point? (b) How high does the ball rise? (c) How
long after projection will the ball have a velocity of 10m/s upward? A velocity of 10m/s
downward? (d) When is the displacement of the ball zero? (e) When is the magnitude of
the ball’s velocity equal to half its velocity of projection? (f) When is the ball‘s
displacement equal to half the maximum height to which it rises? (g) What is the
magnitude and direction of the acceleration while the ball is moving upward? While
moving downward? While at the highest point?
(a) v = 30-9.8t
at highest point, v=0, so t = 9.8/30
(b) h = 30t - 4.9t^2
(c) see (a) when v = 10
(d) displacement = 0 when the ball hits the ground. See (a) which gives half the total flight time
(e) see (a) when v = 15
(f) find t when h = 1/2 of (b)
(g) a = -9.8 at all times, due to gravity