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Find position, velocity vector and the distance attained by an athlete in a long jump event.

The motion of a human body through space can be precisely modelled as the motion of a particle at the body's center of mass, as we will study in Chapter 8. The components of the displacement of an athlete's center of mass from the beginning to the end of a certain jump are described by the two equations

Xf = 0 + (11.2 m/s) (cos 18.5?) t

0.360 m = 0.840 m + (11.2 m/s) (sin 18.5?) t - ½ (9.80 m/s2) t2

Where t is the time at which the athlete lands after taking off at time t = 0. Identify (a) his position and (b) his vector velocity at the take off point. (c) The world long jump record is 8.95 m. How far did the athlete in this problem jump? (d) Make a sketch of the motion of his center of mass.

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