Question

three toy boats with the same mass were in a lake. two boats were moving and one was stopped. each boat got bumped by another boat, but not in the same direction. all the boats changed speed as a result of being bumped. use the information in the diagram to answer. which toy boat(s) experienced the strongest force when it was bumped? how do you know? the blue toy boat experienced the strongest force because it takes a stronger force to slow something down than it takes to speed something up the gray toy boat experienced the strongest force because it had the fastest ending speed the orange and gray toy boats experienced the strongest forces because they both gained the same force as they sped up. the blue boat lost force, so it slowed down. all three toy boats experienced the same strength force because they changed speed by the same amount.

Explanation:

Step1: Recall Newton's second law

Force $F = ma$, where $m$ is mass and $a$ is acceleration. Acceleration $a=\frac{\Delta v}{\Delta t}$. Since the time - interval $\Delta t$ of the bump is the same for all boats and mass $m$ is the same for all boats, the force is proportional to the change in velocity $\Delta v$.

Step2: Calculate change in velocity for each boat

• Blue boat: Initial speed $v_{i - blue}=8\ km/h$, final speed $v_{f - blue}=3\ km/h$. $\Delta v_{blue}=|3 - 8|= 5\ km/h$ (it slowed down).
• Orange boat: Initial speed $v_{i - orange}=0\ km/h$, final speed $v_{f - orange}=5\ km/h$. $\Delta v_{orange}=5 - 0=5\ km/h$ (it sped up).
• Gray boat: Initial speed $v_{i - gray}=12\ km/h$, final speed $v_{f - gray}=17\ km/h$. $\Delta v_{gray}=17 - 12 = 5\ km/h$ (it sped up).

Step3: Compare forces

Since $F = ma$ and $m$ is the same and $a\propto\Delta v$ and $\Delta v_{blue}=\Delta v_{orange}=\Delta v_{gray}=5\ km/h$, all three boats experienced the same strength of force.

Answer:

All three toy boats experienced the same strength force because they changed speed by the same amount.