Question

1. officials are looking into three different ski accidents. the accidents happened when three skiers (all with the same mass) were skiing across flat, snowy ground. they were each bumped by another skier, but not all from the same direction. these skiers changed speed as a result of being bumped. use the information in the diagram to answer.

which skier(s) experienced the strongest force when bumped? how do you know?
a. the skiers in the yellow and purple sweaters; they both gained the same force as they sped up, but the skier in the red sweater lost force and slowed down.
b. the skier in the yellow sweater experienced the strongest force because he has the fastest ending speed.
c. all three skiers experienced the same strength force because they changed speed by the same amount.
d. the skier in the red sweater because it takes a stronger force to slow something down than to speed it up.

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\), and acceleration \(a=\frac{\Delta v}{\Delta t}\). Assuming the time of interaction \(\Delta t\) is the same for all skiers (since the collision - like event of being bumped is a similar - duration interaction), and mass \(m\) is the same for all skiers (given in the problem). The force \(F\) is proportional to the change in velocity \(\Delta v\).

Step2: Calculate the change in velocity for each skier

• For the red - sweater skier: \(\Delta v_{red}=4 - 10=- 6m/s\) (magnitude of change in velocity \(|\Delta v_{red}| = 6m/s\))
• For the yellow - sweater skier: \(\Delta v_{yellow}=12 - 6 = 6m/s\)
• For the purple - sweater skier: \(\Delta v_{purple}=6-0 = 6m/s\)

Since \(F = ma\) and \(a=\frac{\Delta v}{\Delta t}\), with \(m\) and \(\Delta t\) constant for all skiers, the force is directly related to the magnitude of the change in velocity.

Answer:

C. All three skiers experienced the same strength force because they changed speed by the same amount.