A ballplayer standing at home plate hits a baseball that is caught by another player at the same height above the ground from which it is hit. The ball is hit with an initial velocity of 20.6 m/s at an angle of 58.9 degrees above the horizontal. How high will the ball rise?
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To determine how high the ball will rise, we can break down the motion into horizontal and vertical components.
First, let's consider the vertical motion of the ball. We can use the following equation to calculate the maximum height reached by the ball:
h = (v^2 * sin^2θ) / (2 * g)
where:
- h is the maximum height reached by the ball
- v is the initial velocity of the ball (20.6 m/s)
- θ is the angle above the horizontal (58.9 degrees)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Now, let's substitute the given values into the equation:
h = (20.6^2 * sin^2(58.9)) / (2 * 9.8)
Calculating this expression will give us the height.