Explanation:
1. To graphically add vectors, use the tail-to-tip method. Draw the first vector (it doesn't matter which), then draw the second vector where the first vector ends. The resultant vector is from the tail of the first vector to the tip of the second vector.
This graph shows two ways to get the resultant: A + B or B + A.
desmos.com/calculator/bqhcclhhqc
2. To algebraically add vectors, split each vector into x and y components.
Aₓ = 5.0 cos 45 = 3.5
Aᵧ = 5.0 sin 45 = 3.5
Bₓ = 2.0 cos 180 = -2.0
Bᵧ = 5.0 sin 180 = 0
The components of the resultant vector are the sums of the components of A and B.
Cₓ = 3.5 + -2.0 = 1.5
Cᵧ = 3.5 + 0 = 3.5
The magnitude of the resultant vector is found with Pythagorean theorem, and the direction is found with tangent.
C = √(Cₓ² + Cᵧ²) ≈ 3.9 m/s
θ = atan(Cᵧ / Cₓ) ≈ 67°
Answer:
6.67×10¯⁹ A
Explanation:
From the question given above, the following data were obtained:
Quantity of electricity (Q) = 2 μC
Time (t) = 5 mins
Current (I) =?
Next, we shall convert 2 μC to C. This can be obtained as follow:
1 μC = 1×10¯⁶ C
Therefore,
2 μC = 2 μC × 1×10¯⁶ C / 1 μC
2 μC = 2×10¯⁶ C
Next, we shall convert 5 mins to seconds. This can be obtained as follow:
1 min = 60 secs
Therefore,
5 min = 5 min × 60 sec / 1 min
5 mins = 300 s
Finally, we shall determine the current in the circuit. This can be obtained as follow:
Quantity of electricity (Q) = 2×10¯⁶ C
Time (t) = 300 s
Current (I) =?
Q = It
2×10¯⁶ = I × 300
Divide both side by 300
I = 2×10¯⁶ / 300
I = 6.67×10¯⁹ A
Thus, the current in the circuit is 6.67×10¯⁹ A
M = mass of the whale = 1000 kg
m = mass of the seal = 200 kg
V = initial velocity of whale before collision with the seal = 6.0 m/s
v = initial velocity of the seal before collision with the whale = 0 m/s
V' = final velocity of two sea creatures after collision = ?
Using conservation of momentum
M V + m v = (M + m) V'
inserting the above values in the equation
(1000 kg) (6.0 m/s) + (200 kg) (0 m/s ) = (1000 kg + 200 kg) V'
6000 kgm/s + 0 kgm/s = (1200 kg) V'
V' = (6000 kgm/s ) /(1200 kg)
V' = 5 m/s
The half empty will fall quicker
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