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

Question

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. 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 hundredth of a second.

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Tryphena 4 years 2021-08-10T08:42:26+00:00 1 Answers 19 views 0

Answers ( )

  1. phucdien
    0
    2021-08-10T08:43:41+00:00
    Reply

    Answer:

    v_{f} = 74 m/s, F = 230 N

    Explanation:

    We can work on this exercise using the relationship between momentum and moment

            I = ∫ F dt = Δp

    bold indicates vectors

    we can write this equations in its components

    X axis

           Fₓ t = m ( -v_{xo})

    Y axis  

            t = m (v_{yf} – v_{yo})

    in this case with the ball it travels horizontally v_{yo} = 0

    Let’s use trigonometry to write the final velocities and the force

            sin 30 = v_{yf} / vf

            cos 30 = v_{xf} / vf

            v_{yf} = vf sin 30

            v_{xf} = vf cos 30

             sin40 = F_{y} / F

             F_{y} = F sin 40

             cos 40 = Fₓ / F

             Fₓ = F cos 40

    let’s substitute

          F cos 40 t = m ( cos 30 – vₓ₀)

          F sin 40 t = m (v_{f} sin 30-0)

    we have two equations and two unknowns, so the system can be solved

            F cos 40 0.1 = 0.4 (v_{f} cos 30 – 20)

            F sin 40 0.1 = 0.4 v_{f} sin 30

    we clear fen the second equation and subtitles in the first

             F = 4 sin30 /sin40     v_{f}

             F = 3.111 v_{f}

            (3,111 v_{f}) cos 40 = 4 v_{f} cos 30 – 80

            v_{f} (3,111 cos 40 -4 cos30) = – 80

            v_{f} (- 1.0812) = – 80

            v_{f} = 73.99

            v_{f} = 74 m/s

    now we can calculate the force

              F = 3.111 73.99

              F = 230 N

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