Final answer:
To find the maximum height reached by a baseball thrown upward with an initial velocity of 10 m/s from 2 meters, we use kinematic equations under constant acceleration due to gravity. The ball takes 1.02 seconds to reach the peak where its velocity is zero. The total maximum height from the ground is calculated to be 7.1 meters.
Step-by-step explanation:
To determine the maximum height reached by the baseball, which is thrown upward with an initial velocity of 10 m/s from a height of 2 meters, we need to use the following kinematic equation for motion under a constant acceleration due to gravity (g = -9.8 m/s2):
h = v0t + (1/2)at2
Where:
- h is the maximum height above the initial position,
- v0 is the initial velocity,
- t is the time taken to reach maximum height,
- a is the acceleration due to gravity.
At maximum height, the velocity of the baseball will be 0 m/s. Now we will use the kinematic equation for final velocity:
v = v0 + at
0 = 10 m/s + (-9.8 m/s2)t
Solving for t gives t = 10 m/s / 9.8 m/s2 = 1.02 s.
We use this time to find the maximum height above the initial position:
h = 10 m/s (1.02 s) + (1/2)(-9.8 m/s2)(1.02 s)2
h = 10.2 m - 5.1 m
h = 5.1 m
To get the total maximum height from the ground, we add the initial height to the height above the initial position:
Total Maximum Height = Initial Height + H
Total Maximum Height = 2 m + 5.1 m
Total Maximum Height = 7.1 m
Therefore, the maximum height the baseball reaches is 7.1 meters from the ground.