Solve Vectors Problem: Get from A to B Faster

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In summary, the conversation discusses a hypothetical race scenario where the goal is to travel from point A to point B on the other side of a wide river as fast as possible. The racer has a motor boat with a speed of 5m/s, but the river has a current of 2.5m/s. In a practice run where the boat is pointed at a 90 degree angle to the bank, the time it takes to reach point B is discussed. In the second part of the conversation, the racer attempts to reduce their running time to zero by adjusting the direction of the boat. The relevant concepts and equations for this problem involve vector properties, trigonometry, and time calculations. Drawing a picture of the situation is suggested as
  • #1
BilloRani2012
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In a race you are asked to get from A to a particular point B directly opposite
on the other side of a wide river of width 1km as fast as you can. You have a motor
boat that can manage a speed of 5m/s, but the river has a current of 2.5m/s. You
estimate that you can run at 2.5 m/s.

a) In your practice run you head out pointing your boat at an angle of 90 degrees to
the bank. How long does it take you to get from point A to point B?

b) Disgusted by your time you decide to reduce your running time to zero. In what
direction should you point your motor boat? How long will it now take you to get
from point A to point B? Did you make a better time?v
 
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  • #2


What aspect of the problem are you having issues with?
Is there something in particular that doesn't make sense?

What are the relevant equations and concepts to this problem?
How do you think you can get started?
Generally starting by drawing a picture of the situation helps.
 
  • #3


I am also having trouble with this questions similar, it is in part b.
I just don't know how to find the angle the boat needs to head off at to end up at point B.
 
  • #4


Draw the vectors, use vector properties, trig, etc.

Also, this shouldn't be in advanced physics.
 
  • #5


i drew the vectors. so would it be

(2.5-2.5sin30)i + (5-2.5cos30)j

= 1.25i + 2.83j

so, t = distance(m) / vertical velocity
t = 1000 / 2.83
t= 353.3 seconds

is that right?
 
  • #6


by any chance are you doing math1050 at UQ lol
 
  • #7


maybe :D
 

FAQ: Solve Vectors Problem: Get from A to B Faster

How do I determine the direction and magnitude of the vectors in the problem?

The direction of a vector can be determined by its angle and the magnitude can be determined by its length. To find these values, you can use trigonometric functions and the Pythagorean theorem to solve for the components of the vector.

What is the difference between a scalar and a vector in this problem?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. In this problem, the speed of the object would be represented by a scalar, while the velocity (which includes direction) would be represented by a vector.

Can the problem be solved using only one vector?

It depends on the specific problem. In some cases, only one vector may be needed to get from point A to point B faster. However, in more complex problems, multiple vectors may need to be combined to achieve the desired result.

How can I use vectors to find the shortest distance between two points?

In order to find the shortest distance between two points using vectors, you would need to find the difference between the position vectors of the two points. This will give you a vector that points from one point to the other, and its magnitude will be the shortest distance between the two points.

What are some real-life applications of solving vectors problems?

Vectors are used in many different fields, including physics, engineering, and navigation. Some real-life applications include calculating the trajectory of a projectile, designing bridges and buildings, and determining the most efficient route for travel.

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