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 3.8 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.

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 3.8 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

Have you considered using

Vf^2=Vi^2+2ad ?

Answer 2

69mc squared

Answer 3

To find the velocity of the ball at the time of interception, we need to use the kinematic equation that relates initial velocity (u), distance (s), acceleration (a), and final velocity (v):

v^2 = u^2 + 2as

In this case, the initial velocity (u) of the ball is given as 3.8 m/s, the distance (s) it rolls before being intercepted is 5.0 m, and the acceleration (a) is -0.50 m/s^2 (negative because it is decelerating). We need to solve for the final velocity (v).

Plugging the values into the equation, we get:

v^2 = (3.8 m/s)^2 + 2 * (-0.50 m/s^2) * 5.0 m

v^2 = 14.44 m^2/s^2 + (-5.0 m^2/s^2)

v^2 = 14.44 m^2/s^2 - 5.0 m^2/s^2

v^2 = 9.44 m^2/s^2

To find the velocity (v), we take the square root of both sides of the equation:

v = √9.44 m^2/s^2

v ≈ 3.07 m/s

Therefore, the velocity of the ball at the time of interception is approximately 3.07 m/s.