Question

A baseball batter hits a long fly ball, giving it an initial velocity 45.0° above the horizontal. The ball risesto a maximum height of 14.8 m. An outfielder on the opposing team starts running at 7.60 m/s the instantthe ball is hit. Calculate the farthest the fielder can be from where the ball will land so that it is possiblefor him to catch the ball, i.e. distance between fielder's original position and lading of the ball. (16)[HINT: Assume that the outfielder catches the ball at the same height at which it was hit, and that hebegins running at the same time that it was hit.]​

Answer 1

The farthest distance the fielder can be from where the ball will land is approximately 15.5 meters.

To calculate the farthest distance the fielder can be from where the ball will land, we need to determine the time it takes for the ball to reach the ground. Since the outfielder starts running at the same time the ball is hit, the time it takes for the ball to land is also the time it takes for the outfielder to reach the ball. We can use the equation h = v0*t - 0.5*g*t^2 to calculate the time it takes for the ball to reach the ground, where h is the maximum height (14.8 m), v0 is the initial vertical velocity of the ball (which is the same as the initial horizontal velocity), and g is the acceleration due to gravity (9.8 m/s^2).

Using the given information, we can calculate the initial vertical velocity as follows:

v0 = v * sin(theta) = 7.60 m/s * sin(45.0°) ≈ 5.37 m/s

Next, we calculate the time it takes for the ball to reach the ground:

14.8 m = 5.37 m/s * t - 0.5 * 9.8 m/s^2 * t^2

Solving this quadratic equation gives us two possible values for the time: t ≈ 1.34 s or t ≈ 2.39 s. Since the outfielder starts running at the same time the ball is hit, the maximum distance the fielder can be from where the ball will land is the horizontal velocity of the outfielder multiplied by the time it takes for the ball to reach the ground:

distance = v * cos(theta) * t = 7.60 m/s * cos(45.0°) * 2.39 s ≈ 15.5 m

Therefore, the farthest the fielder can be from where the ball will land is approximately 15.5 meters.