The height of a ball that was batted into the air at 150 feet per second is a function of t, the time in seconds after the ball was hit. The height is determined by subtracting 15 times the square of t from 150 times t. Which equation can be used to find t when the ball is 300 feet high?

h = Vo*t + 0.5g*t^2.

150t - 16.2t^2 = 300 Ft.

The height of a ball that was batted into the air at 150 feet per second is a function of t, the time in seconds after the ball was hit. The height is determined by subtracting 15 times the square of t from 150 times t. Which equation can be used to find t when the ball is 200 feet high?

To find the value of t when the ball is 300 feet high, we can set the height function equal to 300 and solve for t.

The given height function is determined by subtracting 15 times the square of t from 150 times t:

Height = 150t - 15t^2

Setting this equal to 300, we have:

150t - 15t^2 = 300

Now, we can rewrite the equation in standard form by moving all terms to one side:

15t^2 - 150t + 300 = 0

To solve this quadratic equation, we can apply various methods such as factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

For a quadratic equation in the form ax^2 + bx + c = 0, the quadratic formula states:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, a = 15, b = -150, and c = 300. Substituting these values into the quadratic formula:

t = (-(-150) ± √((-150)^2 - 4(15)(300))) / (2(15))

Simplifying further:

t = (150 ± √(22500 - 18000)) / 30

t = (150 ± √4500) / 30

Now, let's calculate the values of t separately for the positive and negative square root:

t1 = (150 + √4500) / 30 ≈ 8.97
t2 = (150 - √4500) / 30 ≈ 8.03

Therefore, when the ball is 300 feet high, there are two possible values of t: approximately 8.97 seconds and approximately 8.03 seconds.