Answer:
Here ya gooooooooooooooo
Explanation:
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D.Velocity includes magnitude but not direction.
For this case, what we can do is use the Pythagorean theorem to find the magnitude of the displacement of the car.
We have then
![d ^ 2 = 16 ^ 2 + 12 ^ 2 ](https://tex.z-dn.net/?f=%20d%20%5E%202%20%3D%2016%20%5E%202%20%2B%2012%20%5E%202%0A)
From here, we clear the value of d.
We have then:
![d = \sqrt{16 ^ 2 + 12 ^ 2} ](https://tex.z-dn.net/?f=%20d%20%3D%20%20%5Csqrt%7B16%20%5E%202%20%2B%2012%20%5E%202%7D%20%0A)
Rewriting:
Answer:
The magnitude of the car's displacement is:
d = 20 miles
Answer:
See the answers below.
Explanation:
The total power of the circuit is equal to the sum of the powers of each lamp.
![P=60+100\\P=160 [W]](https://tex.z-dn.net/?f=P%3D60%2B100%5C%5CP%3D160%20%5BW%5D)
Now we have a voltage source equal to 240 [V], so by means of the following equation we can find the current circulating in the circuit.
![P=V*I](https://tex.z-dn.net/?f=P%3DV%2AI)
where:
P = power [W]
V = voltage [V]
I = current [amp]
![I = P/V\\I=160/240\\I=0.67 [amp]](https://tex.z-dn.net/?f=I%20%3D%20P%2FV%5C%5CI%3D160%2F240%5C%5CI%3D0.67%20%5Bamp%5D)
So this is the answer for c) I = 0.67 [amp]
We know that the voltage of each lamp is 240 [V]. Therefore using ohm's law which is equal to the product of resistance by current we can find the voltage of each lamp.
a)
![V=I*R](https://tex.z-dn.net/?f=V%3DI%2AR)
where:
V = voltage [V]
I = current [amp]
R = resistance [ohms]
Therefore we replace this equation in the first to have the current as a function of the resistance and not the voltage.
![P=V*I\\and\\V = I*R\\P = (I*R)*I\\P=I^{2}*R](https://tex.z-dn.net/?f=P%3DV%2AI%5C%5Cand%5C%5CV%20%3D%20I%2AR%5C%5CP%20%3D%20%28I%2AR%29%2AI%5C%5CP%3DI%5E%7B2%7D%2AR)
![60 = (0.67)^{2}*R\\R_{60}=133.66[ohm] \\and\\100=(0.67)^{2} *R\\R_{100}=100/(0.66^{2} )\\R_{100}=225 [ohm]](https://tex.z-dn.net/?f=60%20%3D%20%280.67%29%5E%7B2%7D%2AR%5C%5CR_%7B60%7D%3D133.66%5Bohm%5D%20%5C%5Cand%5C%5C100%3D%280.67%29%5E%7B2%7D%20%2AR%5C%5CR_%7B100%7D%3D100%2F%280.66%5E%7B2%7D%20%29%5C%5CR_%7B100%7D%3D225%20%5Bohm%5D)
b)
The effective resistance of a series circuit is equal to the sum of the resistors connected in series.
![R = 133.66 + 225\\R = 358.67 [ohms]](https://tex.z-dn.net/?f=R%20%3D%20133.66%20%2B%20225%5C%5CR%20%3D%20358.67%20%5Bohms%5D)