MAT200
Franklin College
Erich Prisner
MAT200
Franklin College
Erich Prisner
You can increase your score by solving this challenge. The deadline is Tuesday, February 26. You can also work on this in groups, but everybody involved in the group must be able to present the solution.
A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s.
a) At what speed is his distance from second base decreasing when he is halfway to first base?
b) At what speed is his distance from third base increasing at the same moment?
c) Try to express both these speeds in general (not just for being halfway to first base) in terms of the speed of the batter and his distance from hitting point.
d) Express both speeds in terms of time.
e) Now assume that the hitter doesn't run with constant speed, rather assume that he runs with a constant acceleration of 6 ft/sec2 . Express both speeds in terms of time.
Throughout, please use the following notation: Let x(t) denote the distance from hitting point after time t. y(t) the distance from second base after time t, and z(t) the distance from third base after time t.