A toy rocket is launched from the top of a building 117 feet

A toy rocket is launched from the top of a building 117 feet tall at an initial velocity of 239 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 136 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 is 1612 +239t+ 117 of t s(t) b) The rocket reaches its maximum height of 1009 52 feet after approximately 747 seconds. (Round to the nearest hundredth as needed.) c) The rocket will be more than 136 feet above ground all values of t in the interval l 0799 1486) level for (0 Type your answer in interval notation D not round until the final answer the nearest hundredth as needed)

Solution

s(t)= -16t²+239t +117

b. t is maximum at its vertex that is -b/2a

-(239)/2(-16)= 239/32 = 7.47 secs

c. maximum height s(7.47)=-16(7.47)²+239(7.47)+117=1009.52 feet

c. 136=-16t²+239t +117

t= .08,14.86