Chapter 14.3, Problem 55E

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.

51. A small rocket is fired from a launch pad 10 m above the ground with an initial velocity, in m/s, of 〈300, 400, 500〉. A crosswind blowing to the north produces an acceleration of the rocket of 2.5 m/s².