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.?

Answer 1

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

We have:

# x = 50t # # y=-16t^2+32t #
On the assumption that #t# represents time, and #x# and #y# are the horizontal and vertical displacements respectively in feet then we note that:

Horizontal displacement is linear Vertical displacement is parabolic

So for the vertical displacement to be #6# feet we require:
# -16t^2+32t = 6 # # :. 16t^2 -32t+ 6 = 0#

And using the quadratic formula we form two solutions:

# t = 1+-1/2sqrt(5/2) # # \ \ = 0.2094, 1.7906 \ \ (4dp)#
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Answer 2

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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Answer from HIX Tutor

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.

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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