The addition of vectors involve both magnitude and direction. In this case, we make use of a triangle to visualize the problem. The length of two sides were given while the measure of the angle between the two sides can be derived. We then assign variables for each of the given quantities.
Let:
b = length of one side = 8 m
c = length of one side = 6 m
A = angle between b and c = 90°-25° = 75°
We then use the cosine law to find the length of the unknown side. The cosine law results to the formula: a^2 = b^2 + c^2 -2*b*c*cos(A). Substituting the values, we then have: a = sqrt[(8)^2 + (6)^2 -2(8)(6)cos(75°)]. Finally, we have a = 8.6691 m.
Next, we make use of the sine law to get the angle, B, which is opposite to the side B. The sine law results to the formula: sin(A)/a = sin(B)/b and consequently, sin(75)/8.6691 = sin(B)/8. We then get B = 63.0464°. However, the direction of the resultant vector is given by the angle Θ which is Θ = 90° - 63.0464° = 26.9536°.
In summary, the resultant vector has a magnitude of 8.6691 m and it makes an angle equal to 26.9536° with the x-axis.
Answer:
15 N
Explanation:
According to Newton's third law of motion, to every action, there is an equal and opposite reaction. This reaction is equal in magnitude to the force acting but in an opposite direction.
Now, if the book weighs 15 N, an opposite equal force will be: N = -15 N
But the magnitude of this will be the absolute value which is 15N.
Answer:
(a) Most reactive 
Metal B
Metal D
Metal A
Least reactive Metal C
(b) (i) Bubbles should form very slowly
(ii) No reaction takes place
Explanation:
(a) The given metals arranged in their order of reactivity are;
Most reactive Metal B
Metal D
Metal A
Least reactive Metal C
The other of reactivity is based on the nature of their reactivity of the metals in air
(b) (i) Based on the reactivity of the metals in air, whereby metal A reacts very slowly and an oxide is formed, we have that, based on the reactivity of the metal A, when mixed with dilute hydrochloric acid, bubbles should form very slowly
(ii) Similarly, given that metal C is unreactive, we have that when small pieces of metal C are added to dilute hydrochloric acid, no reaction takes place.
Answer:
water
Explanation:
water is not an element, it is a molecule
