A 3 kg ball is dropped from an airplane 1000 m in the air, traveling west at 245 m/s. What distance in the x-direction did the ball travel in the air as it was falling to the ground?

To find the distance in the x-direction that the ball traveled, we need to calculate the time it took for the ball to fall to the ground and then multiply it by the horizontal velocity.

Explanation:

To find the distance in the x-direction that the ball traveled, we need to calculate the time it took for the ball to fall to the ground. First, let's find the time it took for the ball to reach the ground vertically. We can use the equation[tex]h = (1/2)gt^2,[/tex]where h is the initial height in meters, g is the acceleration due to gravity (9.8 m/s^2), and t is the time it took for the ball to fall:

[tex]1000 = (1/2)(9.8)t^2[/tex]

[tex]t^2 = 1000/4.9[/tex]

t = sqrt(1000/4.9) ≈ 10.1 s

Now that we have the time, we can find the distance in the x-direction by multiplying the time by the horizontal velocity:

Distance = Time * Velocity = 10.1 s * 245 m/s = 2454.5 m