Question

A ball is thrown from an initial height of 1 meter with an initial upward velocity of 11 m/s. The ball's height h (in meters) after t seconds is given by the following.

h=1+11t-5^2
Find all values of t for which the ball's height is 6 meters.
Round your answer(s) to the nearest hundredth.

Answer 1

`t=0.64` and
`t=1.56` seconds

Explanation:

`h=1+11t-5t^2\\\\6=1+11t-5t^2\\\\0=-5+11t-5t^2\\\\0=-5t^2+11t-5\\\\t=(-b\pm√(b^2-4ac))/(2a)\\ \\t=(-11\pm√(11^2-4(-5)(-5)))/(2(-5))\\\\t=(-11\pm√(121-100))/(-10)\\ \\t=(-11\pm√(21))/(-10)\\\\t=(11)/(10)\pm(√(21))/(10)\\ \\t_1\approx0.64\\\\t_2\approx1.56`

Therefore, the values of t for which the ball's height is 6 meters is
`t=0.64` and
`t=1.56` seconds.