A baseball is thrown upward. The path of the baseball models the equation h= -4.9t^2 + 9.2t + 1.6, where h is height of the ball, in metres, after t seconds. How long does it take the baseball to fall to the ground?

Plzzz help

Would the answer be 2.04?

To determine how long it takes for the baseball to fall to the ground, we need to find the value of t when the height (h) of the ball is zero.

In the given equation, h = -4.9t^2 + 9.2t + 1.6.

We can set h equal to zero and solve for t:

-4.9t^2 + 9.2t + 1.6 = 0

To solve this quadratic equation, we can either factor or use the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, a = -4.9, b = 9.2, and c = 1.6. Substituting these values into the formula, we get:

t = (-9.2 ± √(9.2^2 - 4(-4.9)(1.6))) / (2(-4.9))

Simplifying further:

t = (-9.2 ± √(84.64 + 31.36)) / (-9.8)

t = (-9.2 ± √116) / (-9.8)

Now we need to find the values of t by evaluating the expression with both the positive and negative signs:

t₁ = (-9.2 + √116) / (-9.8)
t₂ = (-9.2 - √116) / (-9.8)

Evaluating these values using a calculator, we find:

t₁ ≈ 1.309 seconds (rounded to three decimal places)
t₂ ≈ -0.142 seconds (rounded to three decimal places)

Since time cannot be negative in this context, we discard the negative value. Therefore, the baseball takes approximately 1.309 seconds to fall to the ground.