A ball thrown vertically upward at time t = 0 (s) with initial velocity 80 ft/s and with initial height 96 ft has height function:
a) What is the maximum height attained by the ball?
b) When and with what impact speed does the ball hit the ground?
y(t)= -16t^2+ 80t+ 96
[a] y' (t) = -32t + 80
and this is 0 when t = 80/32 = 2.5 s
[b] now, the ball hits the ground when - 16 t^2 + 80 t + 96 = 0
i.e. at t = 6 s.
the velocity with which the ball hits the ground is therefore y ' (6) = -- 112 ft/s
to find the intervals, find the ...