Find the magnitude and direction for 101m,60.0,85.0m
1 answer:
Answer:
magnitude = 161.3m, ∅ = 32.9°
Explanation:
Vector addition always works the same. Add two vectors by adding their respective components.
vector A:
vector B:
Adding vector A and B:
The magnitude of any vector is given by the Pythagorean theorem:
In the case of the vector A+B:
The angle ∅ of the vector can by found by using trigonometric functions:
For instance, the angle ∅ for a vector is given by the equation:
The direction ∅ can be found by solving the trigonometric function.
In the example of vector A+B:
Solving for ∅:
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1) 148 J
When lifting an object, the work done on the object is equal to its change in gravitational potential energy. Mathematically:
where
mg is the weight of the object
is the change in height
For the box in this problem,
mg = 185 N
Substituting into the equation, we find:
2) (a) 28875 J
The work done by a force applied parallel to the direction of motion of the object is given by
where
F is the magnitude of the force
d is the displacement
In this problem,
F = 825 N is the force applied by the two students together
d = 35 m is the displacement of the car
Substituting,
2) (b) 57750 J
As seen previously, the equation that gives the work done by the force is
We see that the work done is proportional to the magnitude of the force: therefore, if the force is doubled, then the work done is also doubled.
The work done previously was
W = 28875 J
Now the force is doubled, so the new work done will be
3) 4.4 J
In this case, the force acting on the ball is the force of gravity, whose magnitude is:
where
m = 0.180 kg is the mass of the ball
is the acceleration of gravity
Solving the equation,
Now we find the work done by gravity using the same formula applied before:
where d = 2.5 m is the displacement of the ball. We can apply this version of the formula since the force is parallel to the displacement. Substituting,
4) 595.2 kg
In this case, we have the work done on the box:
W = 7.0 kJ = 7000 J
And we also know the change in height of the box:
As we stated in part a), the work done on the box is equal to its change in gravitational potential energy:
Solving for m, we find
And substituting the numerical values, we find the mass of the box:
5) They do the same work
In fact, the net work done by each person on the box is equal to the change in gravitational potential energy of the box:
Where is the difference in height between the final position and the initial position of the box.
This means that the work done on the box depends only on its initial and final position, not on the path taken. The two men carry the box along different paths, however the reach at the end the same position, and they started from the same position: this means that the value of is the same for both of them, so the work they have done is exactly the same.
Answer:
The magnitude of actual velocity is <u>496.67 mph</u> and its direction is <u>51.54° with the x axis in the third quadrant</u>.
Explanation:
Given:
Speed of jumbo jet in southwesterly direction = 550 mph
Velocity of jet stream from west to east direction
First let us draw a vectorial representation of the above velocity vectors.
Consider the south direction as negative y axis and west direction as negative x axis.
From the diagram,
The velocity of the jet can be represented as:
Similarly, the velocity of the stream is,
Now, the vector sum of the above two vectors gives the actual velocity of the aircraft. So, the resultant velocity is given as:
Now, magnitude is given as the square root of sum of the squares of the 'i' and 'j' components. So,
As the horizontal and vertical components of actual velocity negative, the resultant vector makes an angle with the x axis in the third quadrant.
The direction is given as:
Therefore, the magnitude of actual velocity is 496.67 mph and its direction is 51.54° with the x axis in the third quadrant.
