Question

A ball is thrown eastward into the air from the origin (in the direction of the positive x-axis). The initial velocity is 40 i + 32 k, with speed measured in feet per second. The spin of the ball results in a southward acceleration of 4 ft/s2, so the acceleration vector is a = −4 j − 32 k. Where does the ball land?

Answer 1

The ball's motion in the x-direction is uniform, while in the y-direction it is affected by acceleration. By using the equations of motion, we can determine the time it takes for the ball to reach the ground and calculate the horizontal distance it travels.

Step-by-step explanation:

The ball's motion can be analyzed separately in the x and y directions. In the x-direction, the initial velocity is 40 ft/s and there is no acceleration, so the motion is uniform. In the y-direction, the initial velocity is 32 ft/s and the acceleration is -4 ft/s². Using the equations of motion, we can find the time it takes for the ball to reach the ground. Then, by multiplying the x-component of the initial velocity by this time, we can find the horizontal distance the ball travels.