NASA launches a rocket at t = 0 t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.9 t 2 + 205 t + 374 h ( t ) = - 4.9 t 2 + 205 t + 374 .

Question

NASA launches a rocket at  seconds. Its height, in meters above sea-level, as a function of time is given by . 

Answer 1

time it reaches max height is when velocity = 0

v = h' = -9.8t +205 =0

t = 205/9.8 seconds = about 20.918 seconds

max height = h(205/9.8) = -4.9(205/9.8)^2 + 205(205/9.8) + 374

= about 4559.8 meters above sea level