when a hole is made at the bottom of the container then water will flow out of it
The speed of ejected water can be calculated by help of Bernuolli's equation and Equation of continuity.
By Bernoulli's equation we can write

Now by equation of continuity


from above equation we can say that speed at the top layer is almost negligible.

now again by equation of continuity


here we have


now speed is given by


Answer:
The greatest speed of the car is 19.36m/s
Explanation:
The maximum speed the car will attain without skidding is given by:
F= uN = umg ...eq1
But F = mv^2/r
mv^2/r = umg
Dividing both sides by m, leaves you with:
V= Sqrt(ugr)
Where u = coefficient of static friction
g = acceleration due to gravity
r = raduis
Given:
U = 0.82
r=0.82
g= 9.8m/s
V = Sqrt(0.82 × 9.8 × 45)
V = Sqrt(374.85)
V = 19.36m/s
Answer:
x(t) = - 6 cos 2t
Explanation:
Force of spring = - kx
k= spring constant
x= distance traveled by compressing
But force = mass × acceleration
==> Force = m × d²x/dt²
===> md²x/dt² = -kx
==> md²x/dt² + kx=0 ------------------------(1)
Now Again, by Hook's law
Force = -kx
==> 960=-k × 400
==> -k =960 /4 =240 N/m
ignoring -ve sign k= 240 N/m
Put given data in eq (1)
We get
60d²x/dt² + 240x=0
==> d²x/dt² + 4x=0
General solution for this differential eq is;
x(t) = A cos 2t + B sin 2t ------------------------(2)
Now initially
position of mass spring
at time = 0 sec
x (0) = 0 m
initial velocity v= = dx/dt= 6m/s
from (2) we have;
dx/dt= -2Asin 2t +2B cost 2t = v(t) --- (3)
put t =0 and dx/dt = v(0) = -6 we get;
-2A sin 2(0)+2Bcos(0) =-6
==> 2B = -6
B= -3
Putting B = 3 in eq (2) and ignoring first term (because it is not possible to find value of A with given initial conditions) - we get
x(t) = - 6 cos 2t
==>
Answer: λ2= 2.34 * 10^-6 C/m
Explanation: In order to calculate the value of the linear charge density of the insulating shell we have to multiply ρ* Volume of the hollow cylinder, so
Volume of cylinder:2*π*b*L *(b-a) where (b-a) is the thickness, then
λ2=Q/L = 634 *10^-6 C/m^3* 2*π*0.042 m*(0.042-0.26)== 2.34 μ C/m
The average speed of the bus from Lansing to Detroit is

while the average speed of the bus from Detroit to Lansing is

The distance covered by the bus in the two trips is the same (the distance between the two cities), therefore, the average speed of the round trip can be calculated as the mean of the two speeds: