Question

1. three boats were moving across the surface of a smooth lake. the gray and pink boats have the same mass, and both of these boats are more massive than the orange boat. each boat was bumped by another boat, but not from the same direction. use the information in the diagram to answer.

which boat(s) experienced the strongest force when hit? how do you know?
a the gray and pink boats experienced the strongest force because they are both more massive than the orange boat, and they all changed speed by the same amount.
b the pink boat experienced the strongest force because it is as massive as the gray boat and has the highest ending speed.
c all three boats experienced the same force because they changed speed by the same amount.
d the gray boat experienced the strongest force because it takes more force to slow an object than it takes to make it go faster.

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration. Acceleration \(a=\frac{\Delta v}{\Delta t}\). If \(\Delta t\) is the same for all boats (the time of the bump), and we assume \(\Delta v\) (change in speed) is the same for all boats (as per the problem's implicit comparison context - since we are comparing forces based on mass - and no information against this is given), then \(F\propto m\) (force is proportional to mass).

Step2: Analyze boat masses

The gray and pink boats have the same mass and are more massive than the orange boat. Using \(F = ma\), with \(a\) (rate of change of speed, assuming same \(\Delta v\) over same \(\Delta t\)) being the same for all boats (because the problem is set - up to compare based on mass - no info to suggest different \(a\) values from non - mass factors like different bump times), the force is larger for more massive objects.

Answer:

A. The gray and pink boats experienced the strongest force because they are both more massive than the orange boat, and they all changed speed by the same amount.