An astronaut on the moon tosses a ball upwards...?

Question

When will the ball initially be 35 feet above the lunar surface if the ball's height (feet) follows: h(t)=-2.6t^2+32.1t+5.5, and t is in seconds from release?

Answer 1

It's a quadratic:

Even though you do not know (yet) what t is, you know that h(t) = 35

35 = -2.6 t^2  + 32.1 t + 5.5

move things around:

2.6 t^2 - 32.1 t + 29.5 = 0

a = 2.6

b = 32.1

c = 29.5

t = [ -b +/- SQRT( b^2 - 4ac )] / 2a

There are 2 answers

as the rock passes 35 ft on the way up and on the way down

Answer 2

1 second