When a ball is thrown, its height in feet h ..........?

Question

When a ball is thrown, its height in feet h after t seconds is given by the equation

h = vt - 16t^2

where v is the initial upwards velocity in feet per second. If v = 19 feet per second, find all values of t for which h = 5 feet. Do not round any intermediate steps. Round your answer to 2 decimal places.
(If there is more than one answer, enter additional answers with the "or" icon.)

Answer 1

5=19t-16t^2 add 16t^2-19t to each side
16t^2-19t+5=0

t=(19+/-√(361-4*16*5))/32
t=(19+/-√(361-320))/32
t=(19+/-√41)/32
t=(19-√41)/32=0.39 sec
t=(19+√41)/32=0.79 sec

t=0.39 sec and 0.79 sec
t=0.39 sec as the ball is on the way up & t=0.79 sec as the ball is on the way down.

Answer 2

Did you learn about quadratic equations? What you have there is a quadratic equation.

Plug in values and rearrange to get

16t^2 -19t + 5 = 0

Use the quadratic formula (or the POLY key on a TI85 calculator with order=2) to solve.

t = 0.79 | t = 0.39

Answer 3

The quadratic formula is your friend on this one.