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Chapter 4: Problem 57

A baseball is thrown upward from a height of 2 meters with an initial velocity of 10 meters per second. Determine its maximum height.

Short Answer

Expert verified
The baseball reaches its maximum height of approximately 7.12 meters.

Step by step solution

01

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/s虏. Solving for time (t): \( 0 = 10 - 9.8*t \) which gives us \( t = 10/9.8 = 1.02 \) seconds.
02

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/s虏, 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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