Chapter 14.3, Problem 54E

Three-dimensional motion Consider the motion of the following objects. Assume the x-axis points east, the y-axis points north, the positive z-axis is vertical and opposite g, the ground is horizontal, and only the gravitational force acts on the object unless otherwise stated.

1. a. Find the velocity and position vectors, for t ≥ 0.
2. b. Make a sketch of the trajectory.
3. c. Determine the time of flight and range of the object.
4. d. Determine the maximum height of the object.

50. A baseball is hit 3 ft above home plate with an initial velocity of 〈30, 30, 80〉 ft/s. The spin on the baseball produces a horizontal acceleration of the ball of 5 ft/s² in the northward direction.