Find Direction and Angle to arrive directly across initial location?

In summary: Consider e.g. what would happen if the boat's speed relative to the water were less than the speed of the current. In this case, there's no way for the boat to get straight across so you would have to use sin -1 (5/12).
  • #1
Stanc
60
0

Homework Statement


A boat can go 12 km /h in a river that has current of 5 km /h.
At what angle relative to the shore does the boat have to leave to arrive directly across from initial location?


Homework Equations


SOH CAH TOA


The Attempt at a Solution



I just want some explanation of this question. Would my 12km/h be my hypotenuse and the resultant be the straight line across the river perpendicular to the shore or would my 12km/h be the straight line perpendicular to the shore??

Because I get 2 different angles if I use tan-1 (5/12) = 22.16 degrees and sin-1 (5/12) which gives me 24.6 degrees... Which one do I use?
 
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  • #2


No, the 12km/h is the across the river speed and the 5km/h is the river speed so the angle relative to going across the river is tan theta = 5/12. The two speeds add together vectorially giving you a slightly faster speed as you travel across and drift downstream.
 
  • #3


jedishrfu said:
No, the 12km/h is the across the river speed and the 5km/h is the river speed so the angle relative to going across the river is tan theta = 5/12. The two speeds add together vectorially giving you a slightly faster speed as you travel across and drift downstream.

I do not understand this, If I want to end up directly across from my initial point, wouldn't the straight line across the river be my resultant and hypotenuse be my 12km/h??
 
  • #4


Stanc said:
If I want to end up directly across from my initial point, wouldn't the straight line across the river be my resultant and hypotenuse be my 12km/h??
Yes. Consider e.g. what would happen if the boat's speed relative to the water were less than the speed of the current. Now there's no way to get straight across.
 
  • #5


haruspex said:
Yes. Consider e.g. what would happen if the boat's speed relative to the water were less than the speed of the current. Now there's no way to get straight across.

So, I should use sin -1 (5/12)?
 
  • #7


Stanc said:
I do not understand this, If I want to end up directly across from my initial point, wouldn't the straight line across the river be my resultant and hypotenuse be my 12km/h??

Sorry, I misunderstood your question and was looking puely at the math of adding the velocities.
 

Related to Find Direction and Angle to arrive directly across initial location?

1. How do you find the direction and angle to arrive directly across the initial location?

To find the direction and angle, you would need to know the coordinates of the initial location and the desired location. Then, you can use mathematical formulas such as the Pythagorean theorem and trigonometric functions to calculate the angle and direction.

2. Can you explain the concept of direction and angle in relation to arriving directly across the initial location?

Direction refers to the path or bearing that you need to take to reach the desired location, while the angle is the measure of the turn needed to align with the desired direction. It is important to consider both factors to arrive directly across the initial location.

3. What tools or methods can be used to determine the direction and angle to arrive directly across the initial location?

Aside from mathematical formulas, there are also tools such as compasses, protractors, and GPS devices that can assist in finding direction and angle. Additionally, maps and navigation apps can also provide this information.

4. How accurate are the calculations for determining the direction and angle to arrive directly across the initial location?

The accuracy of the calculations depends on the accuracy of the initial coordinates and the tools or methods used. With precise measurements and reliable tools, the calculations can be highly accurate.

5. Can the direction and angle to arrive directly across the initial location change over time?

Yes, the direction and angle can change over time due to factors such as changes in the initial location or environmental conditions. For example, if a road is built in the area, the direction and angle may change as the route to the desired location is altered.

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