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Mandarinka [93]
2 years ago
11

The forces acting on a sailboat are 390 n north and 180 n east. if the boat (including crew) has a mass of 270 kg, what are the

magnitude and direction of its acceleration?
Physics
1 answer:
antoniya [11.8K]2 years ago
4 0
(a) magnitude of acceleration:
we will imagine that the two components of the force are the sides of a right-angled triangle.
We can thus use the Pythagorean theorem to find the magnitude of the force which is the hypotenuses of this triangle
Magnitude of force = sqrt(390^2 + 180^2) = 429.53 Newton,
Using Newton's second law (F=ma), we can find the acceleration as follows:
429.53 = 270 * a 
a = 1.59 m/sec^2

(b) direction of acceleration:
we will again consider the right angled triangle formed from the components of the force.
Using the trigonometric function (tan = opposite / adjacent), we can find the direction of the force as follows:
tan theta = 390 / 180
tan theta = 2.1667
theta = 65.22 degrees 
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Answer:

\boxed {\boxed {\sf 100,000 \ Joules}}

Explanation:

Kinetic energy is energy due to motion. The formula is half the product of mass and velocity squared.

E_k= \frac{1}{2} mv^2

The mass of the roller coaster car is 2000 kilograms and the car is moving 10 meters per second.

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Substitute these values into the formula.

E_k= \frac{1}{2} (2000 \ kg ) \times (10 \ m/s)^2

Solve the exponent.

  • (10 m/s)²= 10 m/s * 10 m/s= 100 m²/s²

E_k= \frac{1}{2} (2000 \ kg ) \times (100 \ m^2/s^2)

Multiply the first two numbers together.

E_k= 1000 \ kg  \times (100 \ m^2/s^2)

Multiply again.

E_k= 100,000 \ kg*m^2/s^2

  • 1 kilogram square meter per square second is equal to 1 Joule.
  • Our answer of 100,000 kg*m²/s² is equal to 100,000 Joules.

E_k= 100,000 \ J

The roller coaster car has <u>100,000 Joules</u> of kinetic energy.

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