# A soccer ball kicked at the goal travels in a path given by the parametric equations: x=50t; #y=-16t^2+32t#, At what two times will the ball be at a height of 6ft.?

time

#= 0.2094, 1.7906 \ \ \ ("unit")\ \ (4dp)#

We have:

Horizontal displacement is linear Vertical displacement is parabolic

And using the quadratic formula we form two solutions:

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To find the times when the ball is at a height of 6 feet, you need to solve the equation -16t^2 + 32t = 6. This equation represents the y-coordinate of the ball at a height of 6 feet.

First, rewrite the equation as -16t^2 + 32t - 6 = 0.

Next, you can solve this quadratic equation using the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a).

For this equation, a = -16, b = 32, and c = -6.

Substitute these values into the quadratic formula and solve for t.

The two solutions you obtain will be the times when the ball is at a height of 6 feet.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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