A baseball is hit at an angle of 45 degrees to the ground with an initial speed of 30 m/s. Find the maximum height reached by the baseball.
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To find the maximum height reached by the baseball, we can use the kinematic equation for vertical motion:
vf^2 = vi^2 + 2ad
In this case, the initial velocity (vi) is 30 m/s and the final velocity (vf) is 0 m/s at the maximum height. The acceleration (a) is -9.8 m/s^2 (due to gravity). We can solve for the displacement (d) which represents the height reached by the baseball.
0 = (30 m/s)^2 + 2(-9.8 m/s^2)d
0 = 900 m^2/s^2 + (-19.6 m/s^2)d
Multiply both sides by -1 to isolate d:
0 = -900 m^2/s^2 + 19.6 m/s^2d
Rearrange the equation:
19.6 m/s^2d = 900 m^2/s^2
Divide both sides by 19.6 m/s^2 to solve for d:
d = 900 m^2/s^2 / 19.6 m/s^2
d = 45.91 m
Therefore, the maximum height reached by the baseball is approximately 45.91 meters.
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