.2.66 A toy rocket is launched from the top of a building 78 feet tall at an ini

Question

.2.66 A toy rocket is launched from the top of a building 78 feet tall at an initial velocity of 151 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 128 feet above ground level? d) After how many seconds will it hit the ground? a) The function that describes the height of the rocket in terms of t is sa)=

Explanation / Answer

a) initial velocity = 151 feet / sec

height of building = 78 feet

so, function becomes

h(t) = - 16t^2 + 151t + 78

b) the rocket will reach its maximum height at

t = -151/ 2(-16)= 4.71875 seconds

maximum height is  - 16(4.71875)^2 + 151(4.71875) + 78 = 434.266 feet

c) 128 =  - 16t^2 + 151t + 78

solving for t

t = 9.094

rocket is 128 feet above ground level for 9.094 seconds

d) 0 =  - 16t^2 + 151t + 78

t = 9.929

rocket will hit the ground after 9.929 seconds

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