Answer:
V₁ = 6 V
, V₂ = V₃ = 3 V
Explanation:
To solve this circuit we must remember that there are two fundamental types of construction in series and parallel.
* a serial circuit there is only one path for current
in this circuit the constant current in the entire circuit and the voltage is the sum of the voltage of each term
* Parallel circuit in this there are two or more paths for the current
in this circuit the voltage is constant and the east is divided between each branch
with these principles let's analyze the proposed circuit
The DC battery is in parallel with resistor R1 and the equivalent of the other branch,
as in a parallel circuit the voltage is constant
V₁ = 6 V
in the other branch (23) it forms a series construction, where the current is constant
6 = iR₂ + iR₃
as they indicate that each resistance has the same value
6 = 2 iR
V = V₂ = V₃ = 3 V
Answer:
a) F = 64.30 N, b) θ = 121.4º
Explanation:
Forces are vector quantities so one of the best methods to add them is to decompose each force and add the components
let's use trigonometry
Force F1
sin 170 = F_{1y} / F₁
cos 170 = F₁ₓ / F₁
F_{1y} = F₁ sin 170
F₁ₓ = F₁ cos 170
F_{1y} = 100 sin 170 = 17.36 N
F₁ₓ = 100 cos 170 = -98.48 N
Force F2
sin 30 = F_{2y} / F₂
cos 30 = F₂ₓ / F₂
F_{2y} = F₂ sin 30
F₂ₓ = F₂ cos 30
F_{2y} = 75 sin 30 = 37.5 N
F₂ₓ = 75 cos 30 = 64.95 N
the resultant force is
X axis
Fₓ = F₁ₓ + F₂ₓ
Fₓ = -98.48 +64.95
Fₓ = -33.53 N
Y axis
F_y = F_{1y} + F_{2y}
F_y = 17.36 + 37.5
F_y = 54.86 N
a) the magnitude of the resultant vector
let's use Pythagoras' theorem
F = Ra Fx ^ 2 + Fy²
F = Ra 33.53² + 54.86²
F = 64.30 N
b) the direction of the resultant
let's use trigonometry
tan θ’= F_y / Fₓ
θ'= 
θ'= tan⁻¹ (54.86 / (33.53)
θ’= 58.6º
this angle is in the second quadrant
The angle measured from the positive side of the x-axis is
θ = 180 -θ'
θ = 180- 58.6
θ = 121.4º
The answer for that is True.
Let the rescue boat starts at an angle theta with the North
now its velocity towards East is given as


now in some time "t" it will catch the boy
so we will have

also we have

now we have



by solving above we got
