What direction should the swimmer swim in this problem?

In summary, the problem involves a swimmer and water with given velocities. The swimmer needs to determine the direction to swim, and has attempted to do so by drawing a velocity vector pointing upwards and another at 38.66 degrees from the horizontal. The correct approach involves completing a vector triangle and using the sine and cosine rules to find the missing angles. The initial attempt had the velocities mixed up, but the correct solution is to find the length and direction of Vw and Vs - Vw, and then use the sine and cosine rules to find the missing angles.
  • #1
Oblivion77
113
0

Homework Statement


Here is the problem.

2ivd09j.png


Homework Equations



Va/b = Va - Vb

The Attempt at a Solution


s - swimmer
w - water

Vw = 0.3m/s
Vs/w = 2.5m/s

therefore, Vs - Vw = 2.5m/s
Vs - 0.3m/s = 2.5m/s
Vs = 2.8m/s

Now I am a bit confused at this point. It is asking which direction the swimmer needs to swim. What I have tried to do is draw 1 velocity vector pointing directly upward (the 0.3m/s one) and another pointing 38.66 degrees from the horizontal (I calculated that angle using the dimensions given). Am I on the right course to solving the problem, or am I completely wrong?
 
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  • #2
Hi Oblivion77! :smile:
Oblivion77 said:
therefore, Vs - Vw = 2.5m/s
Vs - 0.3m/s = 2.5m/s
Vs = 2.8m/s

Nooo …you can't say 2.5 + 0.3 = 2.8 …

relative velocities are vectors, so they add (and subtract) like vectors.
… What I have tried to do is draw 1 velocity vector pointing directly upward (the 0.3m/s one) and another pointing 38.66 degrees from the horizontal (I calculated that angle using the dimensions given). Am I on the right course to solving the problem, or am I completely wrong?

Yes that's fine so far …

now complete the vector triangle …

you know the length and direction of one side, the angle of another side, and the length of the third side …

from that, you should be able to find the other angle(s). :smile:
 
  • #3
Thanks for the response. I was wondering If I have this diagram right?

2502zrl.png


If it's correct would I just then need to solve for the angles? Sorry the drawing isn't really to scale.
 
  • #4
HI Oblivion77! :smile:

(just got up … :zzz:)
Oblivion77 said:
Thanks for the response. I was wondering If I have this diagram right?

If it's correct would I just then need to solve for the angles?

Yes, the diagram is fine (and the arrows are the right way) …

so you know that Vs has length 0.3, and Vw - Vs has length 2.5, and you know one of the angles …

now use the sine rule and the cosine rule. :smile:
 
  • #5
Thanks for the response, doesn't Vw have a length of 0.3 and Vs - Vw = 2.5?
 
  • #6
oops!

Oblivion77 said:
Thanks for the response, doesn't Vw have a length of 0.3 and Vs - Vw = 2.5?

oops! yes, I got them the wrong way round. :redface:
 
  • #7


tiny-tim said:
oops! yes, I got them the wrong way round. :redface:

No problem, thanks for the help.
 

FAQ: What direction should the swimmer swim in this problem?

What is relative velocity?

Relative velocity is the velocity of an object as observed from a different reference point. It is the difference between the velocities of two objects in motion relative to each other.

How is relative velocity calculated?

Relative velocity is calculated by taking the difference between the velocities of the two objects and considering the direction of motion. It can be calculated using vector addition or by using the formula vAB = vA - vB, where vAB is the relative velocity of A with respect to B, vA is the velocity of A, and vB is the velocity of B.

What is the difference between relative velocity and absolute velocity?

The main difference between relative velocity and absolute velocity is that relative velocity takes into account the perspective of the observer, while absolute velocity is measured from a fixed reference point. Relative velocity is dependent on the motion of the observer, while absolute velocity is constant.

How does relative velocity affect collisions?

Relative velocity plays a crucial role in determining the outcome of collisions between objects. The relative velocity at the point of contact between two objects determines the amount of force and energy transferred during the collision. The direction of relative velocity also affects the direction of movement after the collision.

Can relative velocity be negative?

Yes, relative velocity can be negative. This occurs when the direction of motion of the two objects is opposite to each other. In this case, the relative velocity will have a negative value, indicating that the objects are moving away from each other.

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