A water balloon is catapulted into the air so that its height, h, in metres after t seconds is h=-4.9t^2+25t+1.9.

when is the ball 13 m high?

put h=13, put it in standard form

ax^2+bx+c=0
and use the quadratic equation to solve for x.

To find the time when the ball is 13 m high, we need to solve the equation h = 13.

Substituting 13 for h in the given equation, we have:

13 = -4.9t^2 + 25t + 1.9

Rearranging the equation to standard quadratic form, we get:

-4.9t^2 + 25t + 1.9 - 13 = 0

Simplifying further:

-4.9t^2 + 25t - 11.1 = 0

We can solve this quadratic equation using factoring or the quadratic formula. Let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = -4.9, b = 25, and c = -11.1.

Substituting these values into the formula, we get:

t = (-(25) ± √((25)^2 - 4(-4.9)(-11.1))) / (2(-4.9))

Simplifying further:

t = (-25 ± √(625 + 216.24)) / (-9.8)

t = (-25 ± √841.24) / (-9.8)

Calculating the square root:

t = (-25 ± 29.02) / (-9.8)

Solving for both solutions:

t1 = (-25 + 29.02) / (-9.8) ≈ 0.41 seconds
t2 = (-25 - 29.02) / (-9.8) ≈ 5.57 seconds

Therefore, the water balloon will be 13 m high at approximately 0.41 seconds and 5.57 seconds.

To find when the water balloon is 13 meters high, we need to solve the equation -4.9t^2 + 25t + 1.9 = 13 for t.

Here's how you can solve it step by step:

Step 1: Start with the given equation:
-4.9t^2 + 25t + 1.9 = 13

Step 2: Subtract 13 from both sides to isolate the quadratic equation:
-4.9t^2 + 25t + 1.9 - 13 = 0
-4.9t^2 + 25t - 11.1 = 0

Step 3: Now we have a quadratic equation in the form: at^2 + bt + c = 0, where:
a = -4.9, b = 25, and c = -11.1.

Step 4: Apply the quadratic formula to solve for t:
The quadratic formula is t = (-b ± √(b^2 - 4ac)) / (2a).

Plugging in the values, we get:
t = (-25 ± √(25^2 - 4 * -4.9 * -11.1)) / (2 * -4.9)

Step 5: Simplify the equation using a calculator:
t = (-25 ± √(625 - (-217.44))) / (-9.8)
t = (-25 ± √842.44) / (-9.8)
t = (-25 ± 29.02) / (-9.8)

Step 6: Split the equation into two solutions:
Solution 1: t = (-25 + 29.02) / (-9.8)
Solution 2: t = (-25 - 29.02) / (-9.8)

Step 7: Calculate the solutions:
Solution 1: t ≈ 0.402 seconds (rounded to three decimal places).
Solution 2: t ≈ -5.332 seconds (rounded to three decimal places).

Since time cannot be negative in this scenario, we discard Solution 2.

Therefore, the water balloon reaches a height of 13 meters approximately 0.402 seconds after being catapulted.