can someone correct this for me thanks

A ball is thrown upward from the roof of a building 100 m tall with an initial velocity of 20 m/s. Use this information for exercises 35 to 38.
Science and medicine. When will the ball reach a height of 80 m?

h = -5t^2+20t+100

My answer: t= 4.83 s

correct.

To find the time it takes for the ball to reach a height of 80 m, we can use the equation h = -5t^2 + 20t + 100, where h is the height in meters and t is the time in seconds.

Substitute the value of h with 80 and solve for t:

80 = -5t^2 + 20t + 100

Rearrange the equation to form a quadratic equation:

0 = -5t^2 + 20t + 20

Now, to solve the quadratic equation, you can use various methods such as factoring, completing the square, or using the quadratic formula. In this case, the quadratic equation doesn't factor easily, so we will use the quadratic formula.

The quadratic formula is:
t = (-b ± sqrt(b^2 - 4ac)) / 2a

In the equation 0 = -5t^2 + 20t + 20, we have a = -5, b = 20, and c = 20.

Plugging these values into the quadratic formula:

t = (-20 ± sqrt((20)^2 - 4(-5)(20))) / 2(-5)

Simplify the equation further:

t = (-20 ± sqrt(400 + 400)) / -10

t = (-20 ± sqrt(800)) / -10

Now calculate the square root of 800:

sqrt(800) ≈ 28.28

Now substitute this value back into the equation:

t = (-20 ± 28.28) / -10

Now, calculate two separate solutions for t using both the positive and negative roots:

t1 = (-20 + 28.28) / -10 ≈ 0.83 s

t2 = (-20 - 28.28) / -10 ≈ 4.83 s

We have two solutions, t1 ≈ 0.83 s and t2 ≈ 4.83 s.

Since it doesn't make physical sense for the ball to reach a height of 80 m before being thrown, we can discard the negative solution.

Therefore, the time it takes for the ball to reach a height of 80 m is approximately 4.83 s, which is the correct answer.