Response:
The speed at which the distance from the helicopter to you is changing (in ft/s) after 5 seconds is 
ft/ sec
Clarification:
Provided:
h(t) = 25 ft/sec
x(t) = 10 ft/ sec
h(5) = 25 ft/sec. 5 = 125 ft
x(5) = 10 ft/sec. 5 = 50 ft
At this point, we can determine the distance between the individual and the helicopter utilizing the Pythagorean theorem
Now, let's calculate the derivative of distance in relation to time
By plugging in the values for h(t) and x(t) and simplifying, we arrive at,
= 
= ft / sec
a) The force's magnitude is
, and it acts in the direction from south to north, meaning upward. b) The force's magnitude is
, with the direction pointing towards the west. c) The magnitude of the force is
, indicating zero force since the magnetic field aligns parallel to the current (south to north). d) Our conclusion is that the magnetic force is not substantial enough to create impactful consequences at a standard household current of 1.5 A.
Answer:
a) ∆x∆v = 5.78*10^-5
∆v = 1157.08 m/s
b) 4.32*10^{-11}
Explanation:
This problem can be addressed using Heisenberg's uncertainty principle, which is expressed as:
Where h represents Planck’s constant (6.62*10^-34 J s).
Assuming that the electron's mass remains the same, we proceed as follows:
Utilizing the electron's mass (9.61*10^-31 kg) and the uncertainty in position (50 nm), we can compute ∆x∆v and ∆v:
If we treat the electron like a classic particle, the time required to cross the channel is determined using the upper limit of the uncertainty in velocity:
