The function h(t)= 2 + 50t - 1.862t^2, where h(t) is the height in metres and t is the time in seconds, models the height of a golf ball above the planet Mercury's surface during its flight.

Question

a) What is the maximum height reached by the ball
b) How long will the ball be above the surface of Mercury

Answer 1

so you want the vertex of the parabola
the x of the vertex is -b/(2a)
= -50/-3.724 = 13.426..
subbing that back int gives a height of
2+50(13.426..) - 1.862(13.426..)^2 = appr 337.66 m

above "ground" --> h(t) > 0 , for t ≥ 0
solve 2+50t-1.862t^2 = 0
to get t = 26.89 or t = -.0399

so for t ≥ 0 , the time is 26.89 seconds

check:
midway between -.0399 and 26.89 is (26.89-.0399)/2= 13.426..