A toy rocket is launched from the top of a building 114 feet tall at an initial velocity of 167 feet per second

Question

A toy rocket is launched from the top of a building 114 feet tall at an initial velocity of 167 feet per second

a) give the function that describes the height of the rocket in terms of time t

b) determine the time at which the rocket reaches its maximum height, and the maximum height in feet

c) for what time interval will the rocket be more than 122 feet above ground level

d) after ho many seconds will it hit the ground?

the function that describes the height of the rocket in terms of t is s(t)=

Answer 1

a) s(t) = -16t^2 +167t + 114

b) it reaches max height when s'(t) = 0 = -32t +167

t = 167/32

max height = -16(167/32)^2 + 167(167/32) + 114

= -167)^2/64 + (167)^2/32 + 114

= (167)^2/64 + (114)(64)/64

= (281)(167)/64

= about 733.234375 feet high

c) on what interval is it above 122 feet??

122 = -16t^2 +167t + 114

-16t^2 +167t - 8 = 0

t = 167/32 +/- (1/32)sqr(167^2 -64(8)) = the end points of the interval where s> 122 feet

= about 5.22 +/- 165.46/32

= about (0.05, 10.39)

d) when does it hit the ground 0 = -16t^2 + 167t + 114

t 167/32 + (1/32)sqr(167^2 + 64(114)) = about 5.22 + sqr143.06 = 11.08 seconds using the quadratic formula