# Grade 11 Physics Problem - Vectors and Water Currents

## Homework Statement

Sandra needs to deliver 20 cases of celery to the farmer's market directly east across the river, which is 32 km wide. Her boat can move 2.5 km/h in still water. The river has a current of 1.2 km/h flowing downstream, which happens to be moving in a southerly direction.
a) where will Sandra end up if she aims her boat directly across the river?
b) how far will she have to walk to reach the farmer's market?
c) show how sandra could end up at her destination without walking. Include a diagram and calculations.
d) which route will result in the shortest time for sandra to reach her destination? sandra can walk 0.72 m/s when she is pulling her wagon loaded with 20 cases of celery.

## Homework Equations

velocity = displacement/time
SOHCAHTOA

## The Attempt at a Solution

I got the answer to a). I found the time taken to cross in still water (0.0128 h) and multiplied that by the current (2.5 km/h) and got 15.36 m.

For b, c and d I'm confused.

For b, I made a diagram of the journey and it created a triangle with 32 m for the horizontal side and 15.36m for the vertical side. I'm not sure if I'm supposed to use Pythagorean Theory to get the hypotenuse and that will be the distance she needs to walk to reach the market. Or use 0.0128 h and multiply that with a value?

c) I have a feeling she would have to aim upwards to end up at her destination. I know I need to use SOHCAHTOA for this question. If I used the Pythagorean theory like in b) to get the hypotenuse then I could use SOHCAHTOA to find out an angle of the triangle. I'm not sure if the question wants a distance value or angle value.

d) And for this question I am completely lost.

Any help with these questions would be greatly appreciated.

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I got the answer to a). I found the time taken to cross in still water (0.0128 h) and multiplied that by the current (2.5 km/h) and got 15.36 m.
This is correct.

For b, I made a diagram of the journey and it created a triangle with 32 m for the horizontal side and 15.36m for the vertical side. I'm not sure if I'm supposed to use Pythagorean Theory to get the hypotenuse and that will be the distance she needs to walk to reach the market. Or use 0.0128 h and multiply that with a value?
I think you may be overthinking this. If she ends up 15.36 m downstream, that's how far she will have to walk to reach the market.

c) I have a feeling she would have to aim upwards to end up at her destination. I know I need to use SOHCAHTOA for this question. If I used the Pythagorean theory like in b) to get the hypotenuse then I could use SOHCAHTOA to find out an angle of the triangle. I'm not sure if the question wants a distance value or angle value.
Your intuition is right and you are correct that this is basically a trigonometry problem. Knowing that her speed relative to the water is 2.5 km/h, and the current is 1.2 km/h, what angle θ must she make with the "north-east axis" in order for her resultant velocity to point across the river?

Going off what you said for c), and what i drew as a diagram, with 2.5 km/h being the horizontal part of the triangle and 1.2 km/h being the vertical part, I would use arctan(1.2/2.5) and get 25.6 as an angle?

This is correct.

I think you may be overthinking this. If she ends up 15.36 m downstream, that's how far she will have to walk to reach the market.

Your intuition is right and you are correct that this is basically a trigonometry problem. Knowing that her speed relative to the water is 2.5 km/h, and the current is 1.2 km/h, what angle θ must she make with the "north-east axis" in order for her resultant velocity to point across the river?

Not quite. The horizontal part of the triangle is her resultant velocity,or the vector sum of her speed with respect to the water and the current flow with respect to the shore. Her velocity relative to the water should be inclined at some angle with the horizontal, making it the hypotenuse of the triangle.

I m really confuse about vectors when. v find. displacement in vector how do v get to know about which should be taken as first vector n second ,if it's not mention in the question?

verty
Homework Helper
I m really confuse about vectors when. v find. displacement in vector how do v get to know about which should be taken as first vector n second ,if it's not mention in the question?