Answer:

Explanation:
Since the Earth's magnetic field is perpendicular to your direction of motion, the strength of the magnetic force exerted on your head is given by:

where:
is the charge on your head
is the speed at which you are moving
is the strength of the magnetic field of the Earth
By substituting these numbers into the equation, we find the strength of the magnetic force:

Answer:
0.9m/s^2 (yours is 0.87, so choose that)
Explanation:
formula for centripetal acceleration:
v^2/r
to find v, we know that f=1/90s, and r=180m.
v=(2pir)/T
v=(2pi(180))/90
v=12.6m/s
now plug into a=v^2/r
a=(12.6)^2/180
a=0.9m/s^2
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.

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)

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.

![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)
By conservation of momentum, the initial recoil speed of the
rifle is:
u = 904kg * 0.0106 kg / 3.53 kg = 2.7146 m/s
The final recoil speed v is zero in a distance of d = 0.0346 m
So the rifle's acceleration is a = (0 - u^2) / 2*d = -2.7146^2 / 2*.0323
m/s^2
a = -114.07m/s^2