How Far Will a Baseball Travel Before It Reaches the Ground?

Question:

If Fred throws a baseball at 42 m/s horizontally from a height of two meters, how far will the ball travel before it reaches the ground?

Answer:

Using concepts of motion and gravity in physics, we can calculate that a baseball thrown horizontally at 42 m/s from a height of 2 meters will travel approximately 27 meters before hitting the ground.

When analyzing the scenario of a baseball being thrown horizontally from a certain height, we can apply the principles of motion under gravity to determine the distance it will travel before reaching the ground.

Firstly, we need to find the time it will take for the baseball to hit the ground. Given that the height (h) is 2 meters and the acceleration due to gravity (g) is approximately 9.8 m/s², we can use the equation 2gh = t² to calculate the time. By solving for t, we get t = √(2h/g) = √(2*2/9.8) = 0.64 seconds.

Since the horizontal speed (v) of the baseball remains constant at 42 m/s, we can then determine the horizontal distance (d) traveled by the baseball. This can be found by multiplying the velocity by the time, giving us d = v * t = 42 * 0.64 = 26.88 meters. Therefore, the baseball will travel approximately 27 meters before it reaches the ground.

Understanding the physics behind projectile motion and applying the relevant equations allows us to accurately calculate the distance traveled by the baseball in this scenario. This analysis demonstrates the relationship between horizontal speed, time of flight, and vertical height in determining the projectile's trajectory.