Question

A soccer player uses her head to hit a ball up in the air from a height of 2 meters with an initial vertical velocity of 5 meters per second. The height h in meters of the ball is given by h=-4.9t^2+5t+2, where t is the time elapsed in seconds. How long will it take the ball to hit the ground if no other players touch it? Enter the time in two decimal places. Find the amount of real solutions as well

Answer 1

The ball will hit the ground in 1.33 s if no one touches it. The equation has 2 real solutions.

Explanation:

The ball will hit the ground when its height is equal to 0 meters, therefore using this value in the expression and solving for "t" will give us the correct solutions.

`h = -4.9*t^2 + 5*t + 2\\\\-4.9*t^2 + 5*t + 2 = 0\\\\t_(1,2) = (-5 \pm √(5^2 - 4*(-4.9)*(2)))/(2*(-4.9))\\\\t_(1,2) = (-5 \pm √(64.2))/(-9.8)\\\\t_(1,2) =(-5 \pm 8.0125)/(-9.8)\\\\t_1 = (-5 - 8.0125)/(-9.8) = 1.33 \text{ s}\\\\t_2 = (-5 + 8.0125)/(-9.8) = -0.3 \text{ s}`

The ball will hit the ground in 1.33 s if no one touches it. The equation has 2 real solutions.