Question

Suppose that you are viewing a soccer game from a helicopter above the playing field. Two soccer players simultaneously kick a stationary soccer ball on the flat field; the soccer ball has mass 0.420 kg. The first player kicks with force 162 N at 9.0° north of west. At the same instant, the second player kicks with force 215 N at 15° east of south. Find the acceleration of the ball in ˆi and ˆj form.

a) (0.45 m/s² + 1.82 m/s²
b) (1.05 m/s² + 2.23 m/s²
c) (1.82 m/s² + 0.45 m/s²
d) (2.23 m/s² + 1.05 m/s²

Answer 1

To find the acceleration of the soccer ball, we need to calculate the components of the forces applied by each player and then sum up the x-components and y-components of the forces to get the resultant force in each direction. Finally, we divide the resultant forces in each direction by the mass of the ball to obtain the acceleration in the i and j directions.

Step-by-step explanation:

To find the acceleration of the soccer ball, we need to calculate the components of the forces applied by each player. The force from the first player can be broken down into its x-component and y-component. The x-component is -162N * cos(9°) and the y-component is 162N * sin(9°). Similarly, the force from the second player can also be broken down into its x-component and y-component. The x-component is 215N * sin(15°) and the y-component is -215N * cos(15°).

Next, we sum up the x-components and y-components of the forces applied to get the resultant force in each direction. Summing the x-components, we get -162N * cos(9°) + 215N * sin(15°). Summing the y-components, we get 162N * sin(9°) - 215N * cos(15°).

Finally, we divide the resultant forces in each direction by the mass of the ball (0.420kg) to obtain the acceleration in the i and j directions. So, the acceleration of the ball in the î direction is (resultant force in x-direction) / (mass of the ball) and the acceleration in the j direction is (resultant force in y-direction) / (mass of the ball).