Using relative motion (2D) to get rain speed & direction when running

In summary, the person's actual speed is double the initial speed and the direction of rain with vertical is 60°. However, the calculation for VR was incorrect due to errors in using the symbols for vectors and scalar quantities. The correct calculation shows that tanθ = 1/√3 which means θ = 30°.
  • #1
aaronstonedd
6
0

Homework Statement


A person moving towards east with a speed 'v' observes the rain to be falling vertically downwards. When he doubles his speed, the rain appears to come at 30° angle with the vertical. Find the actual speed and direction of rain with vertical.


Homework Equations


Velocity of A with respect to B = Velocity of A – Velocity of B
(VAB = VAVB)


The Attempt at a Solution


Let the actual speed of rain be VR. Let the person's speed be represented by VP.
Using [itex]\widehat{i}[/itex]-[itex]\widehat{j}[/itex]-[itex]\widehat{k}[/itex] notation for vectors, VP = v [itex]\widehat{i}[/itex]

VR = VRsinθ [itex]\widehat{i}[/itex] – VRcosθ [itex]\widehat{j}[/itex]

VRP = VRVP
VRP = VRsinθ [itex]\widehat{i}[/itex] – VRcosθ [itex]\widehat{j}[/itex] – v [itex]\widehat{i}[/itex] = (VRsinθ – v) [itex]\widehat{i}[/itex] –VRcosθ [itex]\widehat{j}[/itex]

∵ Rain is vertically downwards, ∴ (VRsinθ – v) [itex]\widehat{i}[/itex] = 0

So, VRsinθ = v

Now, let VP be 2v [itex]\widehat{i}[/itex].

VRP = VRVP
= +VRsinθ [itex]\widehat{i}[/itex] –VRcosθ [itex]\widehat{j}[/itex] –2v [itex]\widehat{i}[/itex]
= (+VRsinθ –2v) [itex]\widehat{i}[/itex] –VRcosθ [itex]\widehat{j}[/itex]
= –v [itex]\widehat{i}[/itex] –vtanθ [itex]\widehat{j}[/itex]

Now [itex]\frac{-v}{-vtan\theta}[/itex] = tan30° = √3̅

∴ tanθ = [itex]\frac{1}{\sqrt{3}}[/itex]

∴ θ = 60°.

VR = [itex]\frac{2v}{\sqrt{3}}[/itex].


Both these answers are wrong, and I don't know how or why. I'm in Class 11. The correct answers should be θ = 30° and ∴ VR = 2v. What am I missing here?
 
Physics news on Phys.org
  • #2
tan 30° is not the square root of 3.

It is confusing that you use the same symbol for vectors and scalar quantities.
 
  • #3
Two mistakes

Sorry, I made another mistake. Though you're right, sin30° = [itex]\frac{1}{\sqrt{3}}[/itex], I made another mistake: -VRcosθ [itex]\widehat{j}[/itex] ≠ -vtanθ [itex]\widehat{j}[/itex], but, = -vcotθ [itex]\widehat{j}[/itex].

So still, θ = 60°. Why is it so? (I know my answer's wrong, but I don't know why.)
 

1. How does relative motion help determine rain speed and direction?

Relative motion involves observing the movement of objects in relation to one another. By tracking the movement of raindrops in relation to a runner's movement, we can calculate the speed and direction of the rain.

2. What factors affect the accuracy of using relative motion to determine rain speed and direction?

The accuracy of using relative motion is affected by the speed at which the runner is moving, the size and distance of the raindrops, and any wind or other external factors that may impact the movement of the rain.

3. Can relative motion be used to determine the speed and direction of other types of precipitation?

Yes, relative motion can be used to determine the speed and direction of other types of precipitation, such as snow or hail. However, the accuracy may vary depending on the size and movement of the precipitation.

4. How is the data collected and analyzed when using relative motion to determine rain speed and direction?

The data is typically collected by tracking the movement of raindrops in relation to the runner's movement using cameras or other tracking devices. This data is then analyzed using mathematical equations to calculate the speed and direction of the rain.

5. Are there any limitations to using relative motion to determine rain speed and direction?

Yes, there are some limitations to using relative motion. The accuracy may be affected by the size and distance of the raindrops, as well as external factors such as wind. Additionally, the speed and movement of the runner may also impact the accuracy of the calculations.

Similar threads

  • Introductory Physics Homework Help
Replies
6
Views
577
Replies
20
Views
812
  • Introductory Physics Homework Help
Replies
13
Views
2K
Replies
18
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
658
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
11K
  • Introductory Physics Homework Help
Replies
20
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
13K
Back
Top