Grade 10 Math Question

Question

The height of a flare above the ground is given by the formula h = -5t² + 90t + 1, where h is the height in meters and t is the time in seconds.

a) What height the flare was fired from?

b) Calculate the maximum height the flare reaches and the time at which it reaches this height.

c)  Determine the time (to 2 decimal places) the flare hits the ground.

Please show all work for each part. Thank you!

Answer 1

a) 1 meter

b) 406 meters = max height in 9 seconds

c) hits ground in 18.01 seconds

a) the constant term is the intitial height = 1 meter

b) complete the square

-5(t^2 - 18t + 81) + 1 + 81(5) = -5(t-9)^2 + 406

that's in vertex form with vertex = (9, 406) where t=9 seconds to reach the max 406 meters

c) set the equation = 0, 0 is ground level

use the quadratic equation for h, ignore the negative square root

-5t^2 +90t + 1 = 0

t = -90/-10 + (1/10)sqr(8100+20) =about 9+9.01 = 18.01 seconds to reach the ground