the height of an object is given by y(t) = 100t − 16t2

Question

the height of an object is given by

y(t) = 100t − 16t2

with y in feet and t in seconds. Compute the velocity at the instant when t = 2 seconds. Your answer must be accurate to one decimal place.

y '(2) = ___________

Answer 1

y = 100t -16t^2

take the derivative to find velocity

v= y'(t) = 100 -32t

y'(2) = 100-64 = 36 feet per second velocity after 2 seconds

v= exactly 36 ft/sec

if you want to emphasize its accuracy to 1 decimal place, call it 36.0 ft/sec, if you prefer

v(2) = 36.000... ft/sec where the zeros repeat forever.

max height is when v=0, and t = 100/32 = 25/8 =3.125 seconds, y(3.125) = 100(25/8) -16(25/8)^2 = 625/2 - 625/4 = 625/4 = 156.25 feet y(2) = 100(2) - 16(2)^2= 200-64 = 136 feet