To find how long it takes for the soccer ball to fall, we can use the kinematic equation for free fall in the vertical direction:

$t = \sqrt{\frac{2h}{g}}$

Where:

• $t$ is the time it takes to fall,
• $h = 45 \, \text{m}$ is the height of the cliff,
• $g = 9.8 \, \text{m/s}^2$ is the acceleration due to gravity.

Let's plug the values into the equation:

$t = \sqrt{\frac{2 \times 45}{9.8}}$

I'll calculate the time.The time it takes for the soccer ball to fall is approximately $t = 3.03 \, \text{seconds}$.

Therefore, the correct answer is:

A. 3.03 s

Would you like more details, or do you have any questions?

Here are some related questions to expand your understanding:

1. How far would the ball travel horizontally if it was kicked at a different speed?
2. What effect does air resistance have on the horizontal motion of the soccer ball?
3. How would the time change if the cliff was twice as high?
4. What is the final velocity of the ball just before hitting the ground?
5. How can we calculate the horizontal velocity of the ball using the horizontal distance?

Tip: Always separate vertical and horizontal motions when analyzing projectile motion problems.