Assume that you are analyzing the airborne motion of a high jumper who approaches the bar from the right side.  The coordinates of the jumper’s center of gravity (c.g.) at the instant of takeoff (TO) are: (9.840, 8.956, 1.435)m. At an instant when the jumper’s center of gravity is at its highest point (PEAK), the coordinates of the center of gravity are: (8.691, 9.899, 2.335)m.

The X direction is defined as being parallel to the high jump bar and horizontal; the Y direction is also horizontal but perpendicular to the high jump bar; the Z direction is vertical. The coordinates of the base of the right high jump standard are (10.0, 10.0, 0.0)m. A diagram will be provided in class.

From this information, compute the following measures.

1. The velocities of the c.g. in the X, Y and Z directions at the instant of takeoff.
2. The horizontal velocity of the c.g. at the instant of takeoff.
3. The height of the c.g. over the ground when the jumper crosses the plane of the standards.
4. The time between the instants of takeoff and the peak of the jump.
5. The time between the instants of takeoff and the instant when the jumper's c.g. is directly over the bar.
6. The angle of takeoff.
7. These data are from a jump in the 1984 Olympic Trials. For this jump, the height of the bar was 2.34 m (7 feet, 8 inches). If the jumper’s c.g. had to pass above the bar for clearance (a successful jump), did the bar stay up or did it fall? Why?

HINT: You may need to solve for the unknown parameters in a different order than they are listed in questions 1-7.