Answer:
1.) answer B
2.) answer D
3.) answer A
Explanation:
In all of these problems, it is essential to draw pictures in order to understand which trigonometric function to use according to the angle that the vector in question forms with the component requested. For all of them try to picture a right angle triangle with the vector as the hypotenuse, and the components as the triangle's shorter sides. Please refer to the three pictures attached as image for this answer a,d notice that the vector quantity known for all cases is represented in red, and the component to find is represented in green.
Problem 1) : the vector velocity makes an angle of 24 degrees with the edge of the table. So picture that vector as the hypotenuse of a right angle triangle for which you know the value: 1.8 m/s
So in this case, where you know the angle, the hypotenuse, and need to find the adjacent side to the angle, you use the cosine function as follows:
requested component
which we round to 1.6 to match answer C).
For problem 2.) wee need to find the component opposite to the given angle in the triangle for which we also know the hypotenuse. So we use the sine function as follows:
requested component
which we round to 135.9 m to match answer D).
For problem 3.) we need to find the horizontal component to the acceleration which corresponds to the adjacent side to the known angle, so we use the cosine function as follows:
requested component
which we round tp 7.7 to match answer A).
Let us consider two vectors A and B.
As per the question, the two vectors are perpendicular to each other.
Hence the angle between them
We are asked to calculate the resultant of these two vectors.
As per parallelogram law of vector addition, the resultant of two vectors are-
[cos90=0]
This is the way by which we can add two perpendicular vectors.
Answer:
v = 19.6 m/s.
Explanation:
Given that,
The radius of the circle, r = 5 m
The time period of the ball, T = 1.6s
We need to find the ball's tangential velocity.
The formula for the tangential velocity is given by :
Putting all the values in the above formula
So, the tangential velocity of the ball is 19.6 m/s. Hence, the correct option is (c).
First,
where is density,
is mass, and
is volume. We can compute the volume of the roll:
When the roll is unfurled, the aluminum will be a rectangular box (a very thin one), so its volume will be the product of the given area and its thickness . Note that we're assuming the given area is not the actual total surface area of the aluminum box, but just the area of the largest face (i.e. the area of one side of the unrolled sheet of aluminum).
So we have
where is the given area, so
If we're taking significant digits into account, the volume we found would have been , in turn making the thickness
.