A soccer ball is kicked straight upwards with an initial vertical speed of 8.0 meters per second. We can ignore air resistance. How long does it take the ball to have a downwards speed of 4.0 meters per second?

1.22 s

Explanation:

From the question, the ball undergoes a vertical motion.

Applying

g = (v-u) / t ... Equation 1

Where g = acceleration due to gravity, v = final velocity, u = initial velocity, t = time.

make t the subject of the equation

t = (v-u) / g ... Equation 2

Let: The upward be taken as positive direction, and downward be taken as negative direction.

Given: v = 8 m/s, u = - 4 m/s (downward) g = 9.8 m/s²

Substitute into equation 2

t = [8 - (-4) ]/9.8

t = (8+4) / 9.8

t = 12/9.8

t = 1.22 s

1.22 seconds

Explanation:

Given:

final velocity 'vf' = 8 m/s,

initial velocity 'vi' = - 4 m/s (downward, therefore negative)

accalaration due to gravity 'g' = 9.8 m/s²

->As the ball undergoes a vertical motion. using the formula

g = (vf - vi) / t

time 't' = (vf - vi) / g

Substituting all the required values in above eq.

t = 8 - (-4) / 9.8 = > (8+4) / 9.8

t = 12/9.8

t = 1.22 sec

Therefore, it takes 1.22 sec for ball to have a downwards speed of 4.0 meters per second