Question

You kick a soccer ball giving it an initial vertical velocity of 8 m/s. Your foot is 0.10 m above the ground when you kick the soccer ball. Given this information, which equation would you need to use to directly calculate the time it takes for the ball to reach its apex (the top of its trajectory)?

rf - ri = vit + 0.5at^2
vf = vi + at
vf^2= vi^2+ 2a(rf - ri)
v = Δr / Δt

Answer 1

To determine the time needed for the ball to reach its apex after being kicked with an initial velocity of 8 m/s, the appropriate equation is 'vf = vi + at', where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.

Step-by-step explanation:

To calculate the time it takes for a kicked soccer ball with an initial vertical velocity of 8 m/s to reach its apex, you would need to use the equation vf = vi + at. The final velocity (vf) at the apex will be zero because the ball momentarily stops ascending before it starts descending. We know the initial velocity (vi) is 8 m/s, the acceleration (a) due to gravity is -9.8 m/s² (negative because gravity is acting in the opposite direction to the initial velocity), and we are trying to find the time (t).

Using the equation, you set vf to zero and solve for t: 0 = 8 m/s - (9.8 m/s² × t), which results in a time of approximately 0.82 seconds for the ball to reach its apex.