Natalie kicked a soccer ball. The equation h=-16t^2+50t describes the height of the ball (T) seconds after it was kicked. Approximately how many seconds went by before the ball hit the ground?

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Natalie kicked a soccer ball. The equation h=-16t^2+50t describes the height of the ball (T) seconds after it was kicked. Approximately how many seconds went by before the ball hit the ground?

Time, t = 3.125 s

Step-by-step explanation:

The height attained by the ball after it was kicked is given by as a function of time t as :

[tex]h=-16t^2+50t[/tex]

It is required to find the time until which the ball hits the ground. At that point, h(t) = 0

So,

[tex]-16t^2+50t=0\\\\t(-16t+50)=0\\\\t=0, -16t+50=0\\\\t=0, 3.125\ s[/tex]

So, 3.125 seconds before the ball hit the ground.

25/8 or 3.125 seconds

Step-by-step explanation:

To determine the time until the ball hits the ground, you need to solve the quadratic as the height equals zero.

0 = -16t^2+50t

This gives us a classing quadratic that you can factor or use the quadratic formula to solve.

x = 0, x = 25/8

If you graph this, think of y = 0 as the ground, so when the parabola intersects the x-axis on the right that represents how much time would have passed.