Answer:
<em>The magnitude of vector d is 16 and the angle with the x-axis is 270°</em>
Explanation:
<u>Operations With Vectors</u>
Given two vectors in rectangular components:
The sum of the vectors is:
The difference between the vectors is:
The magnitude of 
is:
The angle makes with the horizontal positive direction is:
The question provides the vectors:
Calculate:
The magnitude of 
is:
The angle is calculated by:
The division cannot be calculated because the denominator is zero. We need to estimate the correct angle by looking at the components of the vector. Since the x-coordinate is zero and the y-coordinate is negative, the vector points downwards (south), thus the angle must be -90° or 270° if the range goes from 0° to 360°.
The magnitude of vector d is 16 and the angle with the x-axis is 270°
Work done = force * distance
work done = 200 * 20
work done = 4000J
Answer:
Explanation:
Given
altitude of the Plane 
When Airplane is 
away
Distance is changing at the rate of 
From diagram we can write as
differentiate above equation w.r.t time
as altitude is not changing therefore 
at 
substitute the value we get 
The law of conservation of energy<span>, a fundamental concept of physics, states that the total amount of </span>energy<span> remains constant in an isolated system. It implies that </span>energy<span> can neither be created nor destroyed, but can be change from one form to another.</span>
Answer:
86.51° North of West or 273.49°
Explanation:
Let V' = velocity of boat relative to the earth, v = velocity of boat relative to water and V = velocity of water.
Now, by vector addition V' = V + v'.
Since v' = 6.10 m/s in the north direction, v' = (6.10 m/s)j and V = 100 m/s in the east direction, V = (100 m/s)i. So that
V' = V + v'
V' = (100 m/s)i + (6.10 m/s)j
So, we find the direction,Ф the boat must steer to from the components of V'.
So tanФ = 6.10 m/s ÷ 100 m/s
tanФ = 0.061
Ф = tan⁻¹(0.061) = 3.49°
So, the angle from the north is thus 90° - 3.49° = 86.51° North of West or 270° + 3.49° = 273.49°
