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 \large 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?

Answer 1

Answer:1.32 s

Explanation:

Given

The initial height of ball H=2 m

Initial velocity u=5 m/s

Height of ball at any instant is given by

`H=-4.9t^2+5t+2`

The ball will hit the ground when h=0

`-4.9t^2+5t+2=0\\4.9t^2-5t-2=0\\t=(5\pm√(25+4(4.9)(2)))/(2* 4.9)\\t=(5\pm√(64.2))/(9.8)\\t=(5+8.01)/(9.8)=1.32\ s\quad\text{Neglecting negative value of t}`