A ball is thrown upwards from ground level and reaches a height of "h" metres after "t" seconds, given by the formula h=20t - 5t^2

How about that !

That ball knows to follow the laws of physics.

Is there a question?

t=225

To find the time it takes for the ball to reach a specific height, we can rearrange the equation h = 20t - 5t^2 and solve for t. Let's say we want to find the time it takes for the ball to reach a height of "H" meters.

1. Substitute "H" for "h" in the equation: H = 20t - 5t^2.

2. Rearrange the equation to a quadratic equation form: -5t^2 + 20t - H = 0.

3. Now we have a quadratic equation, which can be solved using the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a).

In this case, a = -5, b = 20, and c = -H. Substituting these values into the quadratic formula, we get:

t = (-(20) ± √((20)^2 - 4(-5)(-H))) / (2(-5)).
= (-20 ± √(400 - 20H)) / (-10).
= (20 ± √(400 - 20H)) / 10.

From here, we have two possible solutions for t. To determine which solution is relevant, consider the physical scenario. Since we are dealing with time, we only consider the positive solution.

Therefore, the time it takes for the ball to reach a height of "H" meters is:
t = (20 + √(400 - 20H)) / 10.

Note: If the quadratic equation has complex solutions (i.e., taking the square root of a negative number), it means that the given height is not achievable by the ball.