A soccer ball of mass 0.4 kg is moving horizontally with a speed of 20 m/s when it is kicked by a player. The kicking force is so large that the ball flies up at an angle of 30 degrees above the ground. The player however claims (s)he aimed her/his foot at a 40 degree angle above the ground. First briefly but precisely explain how this is possible, based on what you heard in the lecture. Then calculate the average kicking force magnitude and the final speed of the ball, if you are given that the foot was in contact with the ball for one tenth of a second.

Explanation:

The ball was moving with velocity of 20 m /s earlier in horizontal direction . Due to kicking, additional V velocity was added to it at 40° because he kicked it at this angle but the ball travelled in the direction of resultant which was making an angle of 30° with the horizontal  .

From the relation of inclination of resultant

Tan θ = V sinα / (u + V cosα) where α is angle between u and V , θ is inclination of resultant

Tan30 =

20 + .766 V = 1.11 V

20 = .344 V

V = 58 m /s

To know the force , we shall apply concept of impulse

F x t = mv  , F is force for time t creating a change of momentum mv

F x .1 = .4 x 58

F = 232 N

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