Grade 11 Physics Problem - Vectors and Water Currents

In summary, the conversation discusses a problem involving delivering celery across a river with a current. The solution involves calculating the time taken to cross the river, the distance the person would have to walk to reach the destination, and the optimal route to take. The solution also involves using trigonometry to determine the angle at which the person should aim their boat in order to end up at the destination. There is also a discussion about vectors and how to determine displacement in vector form.
  • #1
hg10tr
5
0

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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  • #2
hg10tr said:
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?
 
  • #3
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?


Millacol88 said:
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?
 
  • #4
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.
 
  • #5
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?
could anyone of u please help me?
 
  • #6
ammie said:
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?
could anyone of u please help me?

V means voorbeeld? This question is hardly intelligible, but I think here you will find the answer.
 
  • #7
HMM,let me make it clear for example if there is a point p whose position vector is( i hat-2j hat+k hat) n the line of action of force passes through this point and the force F=2i hat -3j hat+4k hat and v have to determine torque about point A whose position. vector is 2i hat+j hat+k hat?
How would we determine. displacement shall we take Alphabetical. order A small and P is big so P-A biz by heat to tail rule A-P the answer coming is nt. correct??
Its really giving me a hell ,and I have an exam so pls if u guys could help?
 

Related to Grade 11 Physics Problem - Vectors and Water Currents

1. What are vectors and how are they used in physics?

Vectors are quantities that have both magnitude and direction. In physics, they are used to represent physical quantities such as displacement, velocity, and force. Vectors are typically represented by arrows, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction of the vector.

2. How do vectors and water currents relate to each other?

Water currents can be represented as vectors, with the direction of the vector indicating the direction of the current and the magnitude representing the speed of the current. This allows us to analyze and predict the movement of water in various scenarios, such as in rivers, oceans, and pipes.

3. How do you calculate the resultant of multiple vectors?

To calculate the resultant of multiple vectors, we use vector addition. This involves breaking down each vector into its horizontal and vertical components, adding the corresponding components together, and then using these values to find the magnitude and direction of the resultant vector.

4. How does the angle of a vector affect its magnitude and direction?

The angle of a vector affects both its magnitude and direction. For a given magnitude, the larger the angle, the smaller the horizontal and vertical components will be and the more the vector will point in the given direction. On the other hand, for a given direction, a larger angle will result in a larger magnitude of the vector.

5. How are vectors and water currents used in real-world applications?

Vectors and water currents are used in a wide range of real-world applications, such as predicting and tracking weather patterns, designing irrigation systems, studying ocean currents, and understanding fluid dynamics in engineering and transportation. They are also used in sports, such as sailing and surfing, to analyze and optimize movement in water.

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