Final answer:
To find the time a soccer ball takes to fall from its peak height of 6m to the ground, use the equation ‘rf - ri = vit + 0.5at^2’ with vi=0, a=-9.81 m/s^2, ri=6m, and rf=0m.
Step-by-step explanation:
To calculate the time it takes for a soccer ball to travel from its peak height to the ground, the most appropriate equation to use is the last one: rf - ri = vit + 0.5at^2. In this case, at the peak (rf), the initial velocity (vi) is zero because the ball is momentarily not moving upward or downward. We know the initial height (ri) as 6 m (the peak height), the final position (rf) is the ground level, hence 0 m. The acceleration (a) is due to gravity and is approximately -9.81 m/s^2 (negative because it's directed downward). Here, we're looking to solve for the time (t), thus the equation simplifies to 0 = 0 + 0.5(-9.81)t^2, which we can rearrange to find the time it takes for the ball to hit the ground. Using this equation, you can directly solve for t without needing any other information about the ball's trajectory.