because blah blah blah blah
The characteristics of the scalar product allows to find the angle between the two vectors is:
The scalar product is the product between two vectors whose result is a scalar.
A . B = |A| |B| cos θ
Where A and B are the vectors, |A| and |B| are the modules of the vectors and θ at the angle between them.
The vector is given in Cartesian coordinates and the unit vectors in these coordinates are perpendicular.
i.i = j.j = 1
i.j = 0
A . B = (4 i - 4j). * -5 i + 7j)
A . B = - 4 5 - 4 7
A. B = -48
We look for the modulus of each vector.
|A| =
|A| =
|A| = 4 √2
|B| =
|B| = 8.60
We substitute.
-48 = 4√2 8.60 cos θ
-48 = 48.66 cos θ
θ = cos⁻¹
θ = 170º
In conclusion using the dot product we can find the angle between the two vectors is:
Learn more about the scalar product here: brainly.com/question/1550649
Answer:
twice the original speed
Explanation:
the centripetal force is the force of an object moving in a circle of turning and it is given by the expression

where f = force of the object
m = mass
v = velocity
r = radius of the circle
first we need to know what the orignal speed will be then we can tell what will happen if the radius of the circle is changed to 4R.
from the expression for the centripetal force, we need to make the velocity subject of the formula

now, if the radius is changed to 4R
in the expression for v above i will need to just insert 4R in place of r

the square root of 4 is 2,
therefore
we can see that this is just twice of what the original speed was.
Answer:
44200 N
Explanation:
To calculate the average force exerted on the car, we will use the following equation

Where F is the average force, t is the time, m is the mass, vf is the final velocity and vi is the initial velocity of the car.
Replacing t = 0.5s, m = 1300 kg, vf = -2 m/s, and vi = 15 m/s and solving for F, we get

Therefore, the average force exerted on the car by the wall was 44200 N