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:
b.false i think
Explanation:
i hope i am correct and helps you
(a)
The formula is:
∑ F = Weight + T = mass * acceleration
as the elevator and lamp are moving downward, I choose downward forces to be
positive.
Weight is pulling down = +(9.8 * mass)
Tension is pulling up, so T = -63
Acceleration is upward = -1.7 m/s^2
(9.8 * mass) + -63 = mass * -1.7
Add +63 to both sides
Add (mass * 1.7) to both sides
(9.8 * mass) + (mass * 1.7) = 63
11.5 * mass = 63
mass = 63 / 11.5
Mass = 5.48 kg
(b)
Since the elevator and lamp are going upward, I choose upward forces to be
positive.
Weight is pulling down = -(9.8 * 5.48) = -53.70
Acceleration is upward, so acceleration = +1.7
-53.70 + T = 5.48 * 1.7
T = 53.70 + 9.316 = approx 63 N
The Tension is still the same - 63 N since the same mass, 5.48 kg, is being accelerated
upward at the same rate of 1.7 m/s^2
Answer:
The arrow is at a height of 500 feet at time t = 2.35 seconds.
Explanation:
It is given that,
An arrow is shot vertically upward at a rate of 250 ft/s, v₀ = 250 ft/s
The projectile formula is given by :
We need to find the time(s), in seconds, the arrow is at a height of 500 ft. So,
On solving the above quadratic equation, we get the value of t as, t = 2.35 seconds
So, the arrow is at a height of 500 feet at time t = 2.35 seconds. Hence, this is the required solution.
Answer:
Explanation:
From the question we are told that
Wind speed
Turbine blade diameter 
Air density 
Mechanical energy 
Generally the power generation potential of the wind turbine X is mathematically given as
Where
Therefore
