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.
To find the velocity of the ball at the time of interception by the South Korean player, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity
a = acceleration
s = distance
Given:
Initial velocity (u) = 4.3 m/s
Acceleration (a) = -0.50 m/s^2 (negative because it is decelerating)
Distance (s) = 5.0 m
Using the equation, we can substitute the given values:
v^2 = (4.3 m/s)^2 + 2(-0.50 m/s^2)(5.0 m)
Now, let's calculate:
v^2 = 18.49 m^2/s^2 + 2(-0.50 m/s^2)(5.0 m)
v^2 = 18.49 m^2/s^2 - 5.0 m^2/s^2
v^2 = 13.49 m^2/s^2
To get the velocity (v), we take the square root of v^2:
v = √13.49 m^2/s^2
Therefore, the velocity of the ball at the time of interception is approximately 3.67 m/s.