Answer:
Power output, P = 924.15 watts
Explanation:
We have the following parameters:
Length of the ramp, l = 12 m
Weight of the individual, m = 55.8 kg
Incline angle with respect to the horizontal, 
Elapsed time, t = 3 s
Let h represent the vertical height of the hill:
h = 5.07 m
Power P required for a person to ascend the hill can be expressed as:
P = 924.15 watts
This indicates that a minimum average power output of 924.15 watts is essential for an individual to ascend this elevation. Thus, this is the answer sought.
Answer:
$ 18.75
Explanation:
Given:
Dave's car has a capacity of 12 gallons.
If the tank is at 3/8 full prior to filling:
The cost of gasoline per gallon is $2.50.
The volume Dave needs to fill:
=
=
of full tank
=
Dave must fill 7.5 gallons.
Total amount Dave will pay:
7.5 gallons x $2.50 =
$ 18.75
Thus, Dave will spend $ 18.75 to completely fill the tank.
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:
Answer:
a) The jogger's acceleration is 1.5 m/s²
b) The car's acceleration is also 1.5 m/s²
c) Yes, the car covers a distance 76 m greater than the jogger.
Explanation:
a) Acceleration is the change in velocity over a given time interval:
a = (final velocity - initial velocity) / time
For the jogger:
a = (3.0 m/s - 0 m/s) / 2.0 s = 1.5 m/s²
b) For the car:
a = (41.0 m/s - 38.0 m/s) / 2.0 s = 1.5 m/s²
c) To find how far the car has traveled after 2 seconds, use the formula for position under acceleration along a straight path:
x = x₀ + v₀ t + ½ a t²
where
x = position at time t
x₀ = initial position
v₀ = initial velocity
t = elapsed time
a = acceleration
Assuming x₀ = 0 (origin at car's starting point):
x = 38.0 m/s × 2 s + ½ × 1.5 m/s² × (2.0 s)²
x = 79 m
Similarly, position of the jogger after 2 seconds is:
x = 0 m/s × 2 s + ½ × 1.5 m/s² × (2.0 s)² = 3 m
The difference traveled by the car compared to the jogger is 79 m - 3 m = 76 m
