A model Rocketlaunched with an initial upward velocity of 201 ft/s. The rockets height h(in feet) after t seconds is given by the following. h=201t-16t^2. Find all values of t for rocket height of 93.

Answer 1

h(t) =-16t^2 +201t

93 = -16^2 +201t

16t^2 -201t +93 =0

use the quadratic formula

t= 201/32+ or - (1/32)sqr(201^2 -4(16)(93))

= about 6.3 + or - 5.8 seconds

= about 0.5 or 12.1 seconds

h(.7) = -16(.5)^2 + 201(.5) = 100.5-4 =96.4

time t = slightly less than half a second

h(12) =-16(12)^2 + 201(12) =2412 - 2304 = 108

time t also = a little more than 12 seconds

max height is when -32t+201 = 0

or t=201/32= about 6.3 seconds

max height = -16(6.3)^2 +201(6.3) = 12,663- 635=

about 12,0028 feet