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
Find the interval on which the function is increasing and decreasing. Sketch the graph of y = f(x), and identify any local maxima and minima. Any global extrema should also be identified.
f(x)=(x-2)^2(x+3)^2© BrainMass Inc. brainmass.com August 15, 2018, 6:06 pm ad1c9bdddf
[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 ...