Answer: 8.1 x 10^24
Explanation:
I(t) = (0.6 A) e^(-t/6 hr)
I'll leave out units for neatness: I(t) = 0.6e^(-t/6)
If t is in seconds then since 1hr = 3600s: I(t) = 0.6e^(-t/(6 x 3600) ).
For neatness let k = 1/(6x3600) = 4.63x10^-5, then:
I(t) = 0.6e^(-kt)
Providing t is in seconds, total charge Q in coulombs is
Q= ∫ I(t).dt evaluated from t=0 to t=∞.
Q = ∫(0.6e^(-kt)
= (0.6/-k)e^(-kt) evaluated from t=0 to t=∞.
= -(0.6/k)[e^-∞ - e^-0]
= -0.6/k[0 - 1]
= 0.6/k
= 0.6/(4.63x10^-5)
= 12958 C
Since the magnitude of the charge on an electron = 1.6x10⁻¹⁹ C, the number of electrons is 12958/(1.6x10^-19) = 8.1x10^24 to two significant figures.
13200N
Explanation:
Given parameters:
Mass = 1100kg
Velocity = 24m/s
time = 2s
unknown:
Braking force = ?
Solution:
The braking force is the force needed to stop the car from moving.
Force = ma = 
m is the mass of the car
v is the velocity
t is the time taken
Force =
= 13200N
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Answer:
2.25 %
Explanation:
65-95-99.7 is a rule to remember the precentages that lies around the mean.
at the range of mean (
) plus or minus one standard deviation (
),
at the range of mean plus or minus two standard deviation,
at the range of mean plus or minus three standard deviation,
So, note that they are asking about the probability that it is greater than 0.32, that is the mean (0.3) plus two times the standard deviation (0.1) (
)
So we know that the 95.5% is between
and
, hence approximately the 4.5% (100%-95.5%) is greater than 0.32 or less than 0.28. But half (4.5%/2=2.25%) is greater than 0.32 and the other half is less than 0.28.
So
Answer:
The distance between knothole and the paint ball is 0.483 m.
Explanation:
Given that,
Height = 4.0 m
Distance = 15 m
Speed = 50 m/s
The angle at which the forester aims his gun are,




Using the equation of motion of the trajectory
The horizontal displacement of the paint ball is


Using the equation of motion of the trajectory
The vertical displacement of the paint ball is



Put the value into the formula


We need to calculate the distance between knothole and the paint ball



Hence, The distance between knothole and the paint ball is 0.483 m.