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A baseball player hits a home run, and the ball lands in the left-field seats, 7.5 m above the point at which it was hit. It lands with a velocity of 36 m/s at an angle of 28° below the horizontal (see Figure 3.13). Ignoring air resistance, find the initial velocity with which the ball leaves the bat.
 | | Figure 3.13
The velocity and location of the baseball upon landing can be used to determine its initial velocity, as Example 8 illustrates.
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Reasoning
To find the initial velocity, we must determine its magnitude (the initial speed v0) and its direction (the angle q in the drawing). These quantities are related to the horizontal and vertical components of the initial velocity (v0x and v0y) by the relations
Therefore, it is necessary to find v0x and v0y, which we will do with the equations of kinematics.
Solution
Since air resistance is being ignored, the horizontal component of the velocity vxremains constant throughout the motion. Thus,
The value for v0y can be obtained from Equation 3.6b and the data displayed below (see Figure 3.13 for the positive and negative directions):
y-Direction Data
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y
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ay
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vy
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v0y
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t
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+7.5 m
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–9.80 m/s2
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(–36 sin 28°) m/s
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?
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In determining v0y we choose the plus sign for the square root, because the vertical component of the initial velocity points upward in Figure 3.13, which is the positive direction. The initial speed v0 and angle q of the baseball are
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