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2 months ago

11

Two vectors A⃗ and B⃗ are at right angles to each other. The magnitude of A⃗ is 4.00. What should be the length of B⃗ so that th

e magnitude of their vector sum is 9.00?

1 answer:

serg [3.5K]2 months ago

8 0

Answer:

B= $\sqrt{65}$ ≅8.06

Explanation:

Applying the Pythagorean theorem:

$C^{2}$ = $A^{2}$ + $B^{2}$

Here, C denotes the hypotenuse length, while A and B signify the lengths of the other two sides of the triangle. We can calculate B's length knowing the hypotenuse is 9 and A is 4.

$9^{2}$ = $4^{2}$ + $B^{2}$

81= 16+ $B^{2}$

81-16= $B^{2}$

B= $\sqrt{65}$ ≅8.06

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13 days ago

The filament of the light bulb is made of tungsten. The resistance of the light bulb at room temperature (20∘C), measured by an

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Explanation:

The formula illustrating the relationship between resistance and temperature is as follows:

R =

$R_{o} + \alpha [T_{2} - T_{1}]$

where, R = final resistance

= initial resistance $R_{o}$

= temperature coefficient of resistivity $\alpha$

= final temperature $T_{2}$

= initial temperature $T_{1}$

Given data as follows.

$T_{1} = (20 + 273) K = 293 K$

R = 36 ohm,

= 3 ohm $T_{2}$

= 0.0045 $R_{o}$

Substituting the provided values into the above formula gives us the following.

R = $\alpha$

36 =

$R_{o} + \alpha [T_{2} - T_{1}]$

=

$3 + 0.0045 \times [T_{2} - 293]$

= 7626.33 K

$T_{2}$ Thus, it can be concluded that $\frac{34.3185}{0.0045}$ the temperature of the light bulb at 12.0 V is 7626.33 K.

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1 month ago

What is the freezing point of radiator fluid that is 50% antifreeze by mass? k f for water is 1.86 ∘ c/m?

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Ethylene glycol is known as the main component found in antifreeze.
The molecular formula for ethylene glycol is C₂H₆O₂.
Its molar mass is calculated as C₂H₆O₂ = (2×12) +(6×1) + (216) = 62g/mol
Given that antifreeze comprises 50% by weight, there exists 1 kg of ethylene glycol mixed with 1 kg of water.
ΔTf = Kf×m
ΔTf refers to the change in the freezing point.
= starting temperature of water - freezing temperature of the solution
= 0°C - Tf
= -Tf
Kf stands for the freezing point depression constant of water, which is 1.86°C/m
m is the molarity of the solution.
=(mass/molar mass) where mass of solvent is in kg
=1000g/62 (g/mol) /1kg
=16.13m
Substituting the value into the equation gives us
-Tf = 1.86 × 16.13 = 30
thus Tf = -30°C

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26 days ago

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A plane flying at 70.0 m/s suddenly stalls. If the acceleration during the stall is 9.8 m/s2 directly downward, the stall lasts

ValentinkaMS [3465]

Answer:

v = 66.4 m/s

Explanation:

We know that the aircraft starts off moving at a speed of

$v = 70 m/s$

now we have

$v_x = 70 cos25$

$v_x = 63.44 m/s$

$v_y = 70 sin25$

$v_y = 29.6 m/s$

in the Y direction, we can apply kinematic equations

$v_y = v_i + at$

$v_y = 29.6 - (9.81 \times 5)$

$v_y = -19.5 m/s$

as there is no acceleration along the x-axis, the velocity in this direction remains unchanged

thus yielding

$v = \sqrt{v_x^2 + v_y^2}$

$v = \sqrt{63.44^2 + 19.5^2}$

$v = 66.4 m/s$

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1 month ago

A bus slows down uniformly from 75.0 km/h to 0 km/h in 21 s. How far does it travel before stopping?

Yuliya22 [3333]

1 hour = 3,600 seconds
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75 km/hour = (75,000/3,600) m/s = 20-5/6 m/s

The mean speed during the deceleration is

(1/2)(20-5/6 + 0) = 10-5/12 m/s.

Traveling at this average speed for 21 seconds,
the bus covers

(10-5/12) × (21) = 218.75 meters.

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2 months ago

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