A cross country team race is about to begin and team Gamma decidesto use their one-dimensional kinematics knowledge that they learnedfrom their first year physics course. Each team consists of twopeople and one horse. The clock is started when the team crossesthe starting line with one of the members (let's call her"Catherine") riding the horse and the other (we'll call him"Jason") on foot.
The rider will of course leave the walker behind. Catherine maytether the horse and continue on foot. When Jason reaches thehorse, he mounts it, rides past Catherine and tethers the horsefurther on and continues walking. When Catherine reaches the horse,she mounts it and rides past Jason. This alternation ofriding/walking continues until the entire team (Catherine, Jasonand the horse) cross the finish line.
Suppose that Catherine walks at a rate of v and Jason (owing to thefact that he has longer legs) walks at a rate of 1.1v. In addition,while Catherine is riding the horse, she moves at a rate of 10.7vand Jason (since he is slightly overweight) rides at a rate of10.0v. (Note also that Jason moves faster on the horse than onfoot). Find the fraction of the total race distance that Catherineshould ride in order to minimize the total race time. Assume thatthe race is sufficiently long that Catherine and Jason canalternate on the horse many times.
A cross country team race is about to begin and team Gamma decidesto use their one-dimensional kinematics knowledge that they learnedfrom their first year physics course. Each team consists of twopeople and one horse. The clock is started when the team crossesthe starting line with one of the members (let's call her"Catherine") riding the horse and the other (we'll call him"Jason") on foot.
The rider will of course leave the walker behind. Catherine maytether the horse and continue on foot. When Jason reaches thehorse, he mounts it, rides past Catherine and tethers the horsefurther on and continues walking. When Catherine reaches the horse,she mounts it and rides past Jason. This alternation ofriding/walking continues until the entire team (Catherine, Jasonand the horse) cross the finish line.
Suppose that Catherine walks at a rate of v and Jason (owing to thefact that he has longer legs) walks at a rate of 1.1v. In addition,while Catherine is riding the horse, she moves at a rate of 10.7vand Jason (since he is slightly overweight) rides at a rate of10.0v. (Note also that Jason moves faster on the horse than onfoot). Find the fraction of the total race distance that Catherineshould ride in order to minimize the total race time. Assume thatthe race is sufficiently long that Catherine and Jason canalternate on the horse many times.
