How Is the Velocity of the Boat Relative to the Earth Calculated?

[courtrigrad]

A boat is traveling 3 m/s relative to the water due north. A current is flowing 4 m/s due east. What is the velocity of the boat relative to the earth? The length of the river is 1000 m. Ok so I used pythogorean theorem and got 5 m/s. Then how would you find the time it takes for the boat to travel the 1000 m? Would it be 3t = 1000, and $t = 333 sec$? This is because you are only looking at the y-component? You couldn't do 5t = 1000?

Thanks

 

[sanitykey]

It depends which way the river runs, if the river runs vertically then 3t=1000 would be correct, however this would be assuming that the east flowing current does not push the boat into the bank and that if the boat does have to turn to avoid crashing into the bank then this takes no time.

If the river runs along the hypotenuse then 5t=1000 would be correct, however this would be assuming that the boat does not resist the east flowing current in any way. If there is no other information in the question i think this is the most probable case.

 

[quicknote]

for sharing your approach to solving this problem. Your use of the Pythagorean theorem to find the boat's velocity relative to the earth is correct. However, to find the time it takes for the boat to travel 1000 m, you need to consider both the x and y components of the boat's velocity.

We can use the formula distance = speed x time to solve for the time it takes for the boat to travel 1000 m.

For the x-component, we have a speed of 4 m/s and a distance of 1000 m. So, we can write 1000 m = 4 m/s x t. Solving for t, we get t = 250 seconds.

For the y-component, we have a speed of 3 m/s and a distance of 1000 m. So, we can write 1000 m = 3 m/s x t. Solving for t, we get t = 333.33 seconds.

Since the boat is traveling in both the x and y directions at the same time, we need to find the time it takes for the boat to travel 1000 m by considering both components. This can be done by taking the average of the two times we calculated, which is (250 + 333.33)/2 = 291.67 seconds.

Therefore, it would take the boat approximately 291.67 seconds to travel 1000 m in the given scenario. I hope this helps clarify the approach to solving this problem.