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18 May, 01:13

Using energy considerations, calculate the average force (in N) a 70.0 kg sprinter exerts backward on the track to accelerate from 2.00 to 9.00 m/s in a distance of 25.0 m, if he encounters a headwind that exerts an average force of 30.0 N against him.

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  1. 18 May, 02:14
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    137.8 N

    Explanation:

    First we need to find the acceleration of the sprinter. To do so, we can use the Torricelli's equation:

    V^2 = Vo^2 + 2*a*S

    9^2 = 2^2 + 2*a*25

    81 = 4 + 50a

    50a = 77

    a = 77/50 = 1.54 m/s2

    Now, to find the resulting force in the sprinter, we can use the following equation:

    Force = mass * acceleration

    Force = 70 * 1.54 = 107.8 N

    If we have a 30 N force against the sprinter, the total force applied is:

    Resulting force = Applied force - Wind force

    107.8 = Applied force - 30

    Applied force = 137.8 N
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