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 was hit. The ball is hit with an initial velocity of 22.3 m/s at an angle of 57.3° above the horizontal. How high will the ball rise?
Question
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 was hit. The ball is hit with an initial velocity of 22.3 m/s at an angle of 57.3° above the horizontal. How high will the ball rise?
Solution
To solve this problem, we can use the equations of motion. The maximum height (H) reached by the projectile can be found using the following formula:
H = (v^2 * sin^2(theta)) / (2 * g)
where:
- v is the initial velocity (22.3 m/s),
- theta is the angle of projection (57.3°), and
- g is the acceleration due to gravity (9.8 m/s^2).
First, convert the angle from degrees to radians: 57.3° = 1 rad.
Then, substitute the given values into the formula:
H = (22.3 m/s)^2 * sin^2(1 rad) / (2 * 9.8 m/s^2)
After calculating the above expression, you will get the maximum height the ball will rise.
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