Projectile motion of a sailboat

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SUMMARY

The discussion focuses on calculating the distances traveled by a sailboat moving at a constant speed of 3.9 m/s in a direction 44 degrees north of west over a period of 23 minutes. The calculations involve using trigonometric functions, specifically cosine and sine, to determine the westward and northward distances. The correct distances are 3900 meters west and 3700 meters north, after converting the total distance from meters to kilometers. The initial error was due to the omission of the unit conversion to kilometers.

PREREQUISITES
  • Understanding of basic trigonometry, specifically sine and cosine functions.
  • Familiarity with unit conversions, particularly between meters and kilometers.
  • Knowledge of projectile motion concepts in physics.
  • Ability to perform calculations involving time and speed.
NEXT STEPS
  • Learn about trigonometric functions in physics applications.
  • Study unit conversion techniques, especially for distance measurements.
  • Explore projectile motion equations and their applications in real-world scenarios.
  • Investigate the effects of wind direction on sailboat navigation and speed.
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and projectile motion, as well as sailing enthusiasts interested in understanding the impact of wind on sailboat travel.

pierra
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Homework Statement



A sailboat runs before the wind with a constant speed of 3.9m/s in a direction 44 north of west.
How far west has the sailboat traveled in 23min ?
How far north has the sailboat traveled in 23min ?
Answer in two sigfigs

Homework Equations



hypothesis*cos(theta)=x
hypothesis*sin(theta)=y


The Attempt at a Solution



23min=1380seconds
3.9*1380=5382(the length of hypothesis)

Sailboat traveled distance of WEST in 23min : 5382*cos(44)=3871.486805
two sigfigs : 3900

Sailboat traveled distance of NORTH in23min: 5382*sin(44)=3738.65136
two sigfigs : 3700

*:multiply

I solve like this but its wrong.
What did I do wrong?
 
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Welcome to PF!

Welcome to PF! :smile:

(it's hypotenuse! :wink: :biggrin:)
pierra said:
A sailboat runs before the wind with a constant speed of 3.9m/s in a direction 44 north of west.
How far west has the sailboat traveled in 23min ?
How far north has the sailboat traveled in 23min ?
Answer in two sigfigs
…
Sailboat traveled distance of WEST in 23min : 5382*cos(44)=3871.486805
two sigfigs : 3900

Sailboat traveled distance of NORTH in23min: 5382*sin(44)=3738.65136
two sigfigs : 3700

hmm … looks ok to me :smile: …

do they want you to convert to km?
 


Thanks for reply!

I forgot to convert that to km. :)
 

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