Problem 57
Question
A baseball is thrown upward from a height of 2 meters with an initial velocity of 10 meters per second. Determine its maximum height.
Step-by-Step Solution
Verified Answer
The baseball reaches its maximum height of approximately 7.12 meters.
1Step 1: Calculate the time taken to reach the maximum height
We utilize the first equation of motion: \( v = u - g*t \). We know from the problem that the velocity (v) becomes zero at the maximum height, the initial velocity (u) is 10 m/s, and the acceleration due to gravity (g) is approximately 9.8 m/s². Solving for time (t): \( 0 = 10 - 9.8*t \) which gives us \( t = 10/9.8 = 1.02 \) seconds.
2Step 2: Calculate the maximum height
Now, using the second equation of motion: \( h = u*t - 1/2*g*t^2 \), where u=10 m/s, g=9.8 m/s², t=1.02 sec, and the initial height is 2 m, we can solve for (h): \( h = 10*1.02 - 1/2*9.8*1.02^2 + 2 \) which gives approximately \( h = 7.12 \) meters. This is the maximum height the ball reaches.
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