Answer:at 21.6 min they were separated by 12 km
Explanation:
We can consider the next diagram
B2------15km/h------->Dock
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B1 at 20km/h
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V
So by the time B1 leaves, being B2 traveling at constant 15km/h and getting to the dock one hour later means it was at 15km from the dock, the other boat, B1 is at a distance at a given time, considering constant speed of 20km/h*t going south, where t is in hours, meanwhile from the dock the B2 is at a distance of (15km-15km/h*t), t=0, when it is 8pm.
Then we have a right triangle and the distance from boat B1 to boat B2, can be measured as the square root of (15-15*t)^2 +(20*t)^2. We are looking for a minimum, then we have to find the derivative with respect to t. This is 5*(25*t-9)/(sqrt(25*t^2-18*t+9)), this derivative is zero at t=9/25=0,36 h = 21.6 min, now to be sure it is a minimum we apply the second derivative criteria that states that if the second derivative at the given critical point is positive it means here we have a minimum, and by calculating the second derivative we find it is 720/(25 t^2 - 18 t + 9)^(3/2) that is positive at t=9/25, then we have our answer. And besides replacing the value of t we get the distance is 12 km.
The distance an object falls from rest through gravity is
D = (1/2) (g) (t²)
Distance = (1/2 acceleration of gravity) x (square of the falling time)
We want to see how the time will be affected
if ' D ' doesn't change but ' g ' does.
So I'm going to start by rearranging the equation
to solve for ' t '.
D = (1/2) (g) (t²)
Multiply each side by 2 : 2 D = g t²
Divide each side by ' g ' : 2 D/g = t²
Square root each side: t = √ (2D/g)
Looking at the equation now, we can see what happens
to ' t ' when only ' g ' changes:
-- ' g ' is in the denominator; so bigger 'g' ==> shorter 't'
and smaller 'g' ==> longer 't' .
-- They don't change by the same factor, because 1/g is inside
the square root. So 't' changes the same amount as √1/g does.
Gravity on the surface of the moon is roughly 1/6 the value
of gravity on the surface of the Earth.
So we expect ' t ' to increase by √6 = 2.45 times.
It would take the same bottle (2.45 x 4.95) = 12.12 seconds
to roll off the same window sill and fall 120 meters down to the
surface of the Moon.
Answer:
The magnitude of the electric flux is 
Explanation:
Given that,
Electric field = 2.35 V/m
Angle = 25.0°
Area 
We need to calculate the flux
Using formula of the magnetic flux
Where,
A = area
E = electric field
Put the value into the formula
Hence, The magnitude of the electric flux is
Answer:
In the more scientific viewpoint, the most important thing that she must do is caring for her hygiene and put some plastic gloves in her hands.
This is because there are lots of particles that can be retained in the hands (dust, skin, etc), and when examining the scene, she may drop some of these particles, "contaminating" the scene in this way with information that only will affect the investigation.
So the most important thing is being prepared to not affect anything in the crime scene
Answer:
568.18 N
Explanation:
From the question,
The formula for gravitational potential is given as
Ep = mgh........................ Equation 1
Where Ep = Gravitational potential, m = mass of the diver,h = Height.
But,
W = mg.................... Equation 2
Where W = weight of the diver.
Substitute equation 2 into equation 1
Ep = Wh
Make W the subject of the equation
W = Ep/h................... Equation 3
Given: Ep = 25000 J, h = 44 m
Substitute into equation 3
W = 25000/44
W = 568.18 N.
Hence the weight of the diver = 568.18 N
