Object on Earth with initial velocity.

Question

An object on Earth is project upward with initial velocity of 32 ft per sec, then its height after t seconds is given by h(t) = 16t² + 32t.

a. Find the maximum height attained by the object algebraically.

b. How many seconds does it take for the object to hit the ground? Solve by factoring.

c. How many seconds does it take for the object to hit the ground? Solve by using the quadratic formula.

Answer 1

max h is when h'=0 = 32t +32 = 0, t=1 second, max h = 16+32 = 48 feet

hits the ground in twice time for max h, so 2 seconds

16t^2 +32 = 16t(t+2) = 0, t = 0 and t=-2

using quadratic formula

t = -32/32 + or - (1/32)sqr(32^2 -4(16)(0)) = -1 + or - 32/32 = -2 or 0