Projectile motion of a sailboat

In summary, the sailboat traveled approximately 3.9 km west and 3.7 km north in 23 minutes at a constant speed of 3.9m/s in a direction 44 north of west. The calculations were based on the equations hypothesis*cos(theta)=x and hypothesis*sin(theta)=y, with a result of 3900 meters west and 3700 meters north, rounded to two significant figures.
  • #1
pierra
3
0

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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  • #2
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?
 
  • #3


Thanks for reply!

I forgot to convert that to km. :)
 

FAQ: Projectile motion of a sailboat

What is projectile motion?

Projectile motion is the motion of an object that is launched or thrown into the air and is subject to the force of gravity. It follows a curved path, known as a parabola, and is influenced by both horizontal and vertical components.

How does projectile motion apply to sailboats?

Sailboats experience projectile motion when they are sailing on the water. The force of the wind pushing against the sail causes the boat to move forward, and gravity pulls the boat down towards the water. This results in a curved path of motion for the sailboat.

What factors affect the projectile motion of a sailboat?

The main factors that affect the projectile motion of a sailboat are the force of the wind, the weight and design of the boat, and the angle of the sail. The wind speed and direction can also impact the motion of the boat.

How is the velocity of a sailboat calculated during projectile motion?

The velocity of a sailboat during projectile motion can be calculated using the formula v = √(2gh), where v is the velocity, g is the acceleration due to gravity, and h is the height of the sailboat above the water. This formula takes into account the horizontal and vertical components of the boat's motion.

What is the maximum height a sailboat can reach during projectile motion?

The maximum height a sailboat can reach during projectile motion depends on several factors, including the initial velocity, the angle of the sail, and the force of the wind. It is possible for a sailboat to reach a height of several meters, but this also depends on the design and weight of the boat.

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