Anonymous
Anonymous asked in Science & MathematicsPhysics · 3 weeks ago

Physics Question- HELP!?

A soccer ball player bounces the ball off her head, changing the velocity of the ball. She changes the x-component of the velocity of the ball from vix = 7.9 m/s to vfx = 5.9 m/s and the y-component from viy =−1.4 m/s to vfy = 4.2 m/s. If the ball has a mass of 0.45 kg and is in contact with the player's head for 7.1 ms, determine the following.

(a)direction of the impulse (in degrees counterclockwise from the +x-axis) delivered to the ball° counterclockwise from the +x-axis

(b)

magnitude of the impulse (in kg · m/s) delivered to the ball kg · m/s

2 Answers

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  • 3 weeks ago

    impulse = change in momentum

    delta(p) = m delta(v) = (0.45(-2.0) + 0.45(5.6) i)

    I'll use a vector calculator to convert this to R, theta

    (-0.90 + 25.2 i) = 25.2 @ 92°

    so

    magnitude is 25.2 kg*m/s

    and direction is 92° CCW from +x-axis or 2° past vertical

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  • 3 weeks ago

    Pi = m*(vix i_hat + viy j_hat)

    Pf = m*(vfx i_hat + vfy j_hat)

    DP = Pf - Pi = m*((vfx - vix) i_hat + (vfy - viy) j_hat)

    Impulse I = DP/dt = 63.38 kg/s ((vfx - vix) i_hat + (vfy - viy) j_hat)

    = 63.38 kg/s*(-2 m/s i_hat + 5.6 m/s j_hat) = -126.8 i_hat + 354.9 j_hat N

    Angle wrt to x - axis of I: q = arctan(354.9/(-126.8) = -70.35 degrees

    magnitude of I = sqrt((-126.8)^2 +354.9^2) = 376.9 N

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