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An arrow is shot vertically upward at a rate of 180 feet per second from ground level. Use the projectile formula [tex]h = -16t^2 + v_0 t + h_0[/tex] to determine when the height of the arrow will be 330 feet.

Recall that [tex]v_0[/tex] is the initial velocity of the object and [tex]h_0[/tex] is the initial height of the object.

Answer: The arrow is at 330 feet after

Note: Round any numerical responses to two decimal places. If there are multiple answers, separate them with commas.

Answer :

To determine when the height of the arrow will be 330 feet, we can use the projectile formula h = -16t² + v₀t + h₀, where h is the height, t is the time, v₀ is the initial velocity, and h₀ is the initial height. Given that the arrow is shot vertically upward at a rate of 180 feet per second, we can substitute the values into the formula to solve for t.

We have the equation h = -16t² + v₀t + h₀, where h is the height, t is the time, v₀ is the initial velocity, and h0 is the initial height. In this case, h₀ is the ground level and is equal to 0.

Substituting the given values into the equation, we have:

330 = -16t² + 180t

Rearranging the equation to form a quadratic equation in standard form, we get:

16t² - 180t + 330 = 0

Now, we can solve this quadratic equation for t using methods such as factoring, completing the square, or using the quadratic formula. Once we find the values of t, we can determine when the height of the arrow will be 330 feet.

Since the quadratic equation might have two solutions, we need to consider the positive value of t, as time cannot be negative. The resulting value of t will indicate the time at which the height of the arrow will be 330 feet.

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