(time given is the total time in the air)
During a baseball game, a batter hits a high pop-up.
If the ball remains in the air for 4.5 s, how high does it rise? The acceleration of gravity is 9.8 m/s^2.
Answer in units of m
To determine the height the ball reaches, we can use the equation of motion for vertical motion. The equation is:
h = v₀t + (1/2)at²
Where:
- h is the height
- v₀ is the initial vertical velocity (which is 0 since the ball starts at its highest point)
- t is the time in the air
- a is the acceleration due to gravity (-9.8 m/s² since it is acting in the opposite direction of the ball's motion)
In this case, we are given the time of 4.5 seconds. We can plug in these values into the equation:
h = 0(4.5) + (1/2)(-9.8)(4.5)²
Simplifying the equation:
h = (1/2)(-9.8)(4.5)²
Now, we can solve for h using a calculator:
h ≈ (1/2)(-9.8)(20.25)
h ≈ -98.1
Since height cannot be negative, we take the absolute value to get the magnitude of the height:
h ≈ 98.1
Therefore, the ball rises to a height of approximately 98.1 meters.