Your nerf dart gun is able to shoot a suction cup dart at a speed of 5 m/s. Your room is 3 meters across. You want to shoot your
dart gun horizontally and hit the bulls-eye. How high above the bullseye would you need to aim for the dart to hit the spot you desire?
1 answer:
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Answer:
The doppler effect equation is:
In the equation we have frequencies, but then we have the wavelengths of the lights, remember the relation:
v = f*λ
then:
f = v/λ
and v is the speed of light, then:
f = c/λ
where:
f' is the observed frequency, in this case, is equal to f = (3*10^17nm/s)/550 nm
f is the real frequency, in this case, is (3*10^17nm/s)/650 nm
vs is the speed of the source, in this case, the source is not moving, then vs = 0 m/s.
v is the speed of the wave, in this case, is equal to the speed of light, v = 3*10^8 m/s
v0 is your speed, this is what we want to find.
Replacing those quantities in the equation, we get:
(3*10^17nm/s)/550 = (3*10^8 m/s + v0)/(3*10^8 m/s)*(3*10^17nm/s)/650 nm
(650nm)/(550nm) = (3*10^8 m/s + v0)/(3*10^8 m/s)
1.182*(3*10^8 m/s) = (3*10^8 m/s + v0)
1.182*(3*10^8 m/s) - (3*10^8 m/s) = v0 = 54,600,000 m/s
So your speed was 54,600,000 m/s, which is a lot.
Our values can be defined like this,
The problem can be solved for part A, through the Work Theorem that says the following,
Where
KE = Kinetic energy,
Given things like that and replacing we have that the work is given by
W = Fd
and kinetic energy by
So,
Clearing F,
Replacing the values
B) The work done by the wall is zero since there was no displacement of the wall, that is d = 0.