Well, if the baseball player hits the ball and it leaves the bat at an angle of 30.0 degrees, it sounds like the ball is really trying to take off and fly away!
As for how far it will travel in the air, we can use some good old physics to figure it out.
First, we need to break down the velocity of the ball into its vertical and horizontal components. The horizontal component will determine how far the ball travels, while the vertical component will determine how high it goes before coming back down to earth.
The vertical component can be found by multiplying the initial velocity (40.0 m/s) by the sine of the launch angle (30.0 degrees). So, the vertical component is 40.0 m/s * sin(30.0 degrees) = 20.0 m/s.
Now, the horizontal component can be found by multiplying the initial velocity (40.0 m/s) by the cosine of the launch angle (30.0 degrees). So, the horizontal component is 40.0 m/s * cos(30.0 degrees) = 34.64 m/s.
Since the ball will travel in the air until it hits the ground, we are only concerned with the horizontal distance. So, to determine how far it will travel, we can use the horizontal component of velocity (34.64 m/s) and the total time the ball is in the air.
The time it takes for the ball to hit the ground can be found using the equation: time = (2 * vertical component of velocity) / gravitational acceleration. Since we're on Earth, the gravitational acceleration is approximately 9.8 m/s^2.
So, the time it takes for the ball to hit the ground is:
time = (2 * 20.0 m/s) / 9.8 m/s^2 ≈ 4.08 seconds.
Now that we know the time, we can calculate the distance the ball will travel horizontally by multiplying the horizontal component of velocity (34.64 m/s) by the time (4.08 seconds).
So, the distance the ball will travel in the air is approximately:
distance = 34.64 m/s * 4.08 seconds ≈ 141.43 meters.
Therefore, the ball will travel about 141.43 meters in the air before it comes back down to Earth. But hey, who needs math when you can just watch it on TV and cheer for your favorite team?