Question

The United States and South Korean soccer teams are playing in the first round of the World Cup. An American kicks the ball, giving it an initial velocity of 4.3 m/s. The ball rolls a distance of 5.0 m and is then intercepted by a South Korean player. If the ball accelerates at −0.50 m/s2 while rolling along the grass, find its velocity at the time of interception.

Answer 1

Vf = 3.67 [m/s]

Step-by-step explanation:

To solve this problem we must use the following equation of kinematics.

`v_(f) ^(2) =v_(i) ^(2) -(2*a*x)`

where:

Vf = final velocity [m/s]

Vi = initial velocity = 4.3 [m/s]

a = acceleration or desacceleration = 0.5 [m/s²]

x = distance = 5 [m]

Note: The negative sign in the above equation means that the velocity of the ball is decreasing (desacceleration).

Now replacing:

Vf² = (4.3)² - (2*0.5*5)

Vf² = 18.49 - 5

Vf² = 13.49

using the square root, we have.

Vf = 3.67 [m/s]