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George Brett, after hitting what he thought was a go-ahead home run for Kansas City, was ruled out because the sticky pine tar on his bat had spread too far up the handle. Suppose that the ball hit the bat on one of the areas with pine tar. Explain how the ball could get extra spin and travel farther because of the pine tar. 4, the Magnus force direction turned out to be exactly opposite the direction of the motion of the back of the ball (the arrows). This is true in general. Illustrate this for two other arrow directions.

8 s, Projectile Motion 15 respectively. The backspin on the hit gives the ball extra height, extra hang time, and extra distance. 9 has to do with symmetry. The “gravity” graph has symmetry; the flight up is the same as the flight down. In the “+drag” graph, you may notice that the flight down is shorter than the flight up; since drag is reducing the speed, less distance is covered later in the flight. The “+Magnus” graph is also asymmetric, with the peak of the graph occurring at about the 60% mark of horizontal distance.

This explanation makes it clear that the greater the spin rate of the ball, the greater the Magnus force. The Magnus force depends on both the velocity of the ball and its spin vector, defined as follows. Consider a ball with a horizontal velocity directly away from you. 4. 4: Spin called backspin and is the most common spin in sports. We define a spin vector s by first identifying the axis about which the ball rotates. In this example, the spin axis is a left-right horizontal axis through the center of the ball.