What is your friends speed relative to you?

[dashkin111]

Homework Statement

There's a 100m wide river, with a current of 8.5 m/s going 45 degrees SE. You and a friend are standing directly opposite each other across the river, the friend on the north side, you on the south side. You each get in boats that travel 7 m/s relative to the water and head out directly north/south.

a. What is your friends speed relative to you?

...
d. How long does it take to cross the river?

Homework Equations

The Attempt at a Solution

Just looked over briefly at some of them, can someone verify if these look correct?

A is 14 m/s

D Since you will be traveling 1 m/s north (the current vector will push 6 m/s down on you), it will take 100 s to cross it.

 

[mjsd]

looks fine to me

 

[ogb p]

I would first clarify the question by asking for more specific information. Are we assuming that the boats are traveling at a constant speed of 7 m/s throughout the entire crossing? Are we taking into account the effects of the current on the boats? These details will impact the accuracy of our calculations.

Assuming the boats are traveling at a constant speed of 7 m/s and the current is not affecting the boats, then your friend's speed relative to you would be 7 m/s. This is because you are both traveling in opposite directions at the same speed of 7 m/s, making your relative speed 14 m/s.

However, if we take into account the current, then your friend's speed relative to you would be slightly less than 7 m/s. This is because the current is pushing your friend's boat in a southeasterly direction, slightly reducing their northward speed relative to you.

To calculate the exact speed, we would need to use vector addition and take into account the magnitude and direction of the current. This would result in a slightly lower relative speed for your friend compared to the first scenario.

As for the time it takes to cross the river, it would also depend on the factors mentioned above. If we assume a constant speed of 7 m/s and no effect from the current, then it would take approximately 14.3 seconds to cross the river (100 meters / 7 m/s = 14.3 seconds).

In conclusion, as a scientist, I would make sure to gather all necessary information and clarify any assumptions before providing an accurate response to the question.