Consider steady and incompressible liquid (water) flowing from a large tube through a dam. The water fell distance h from the surface of the reservoir and if we assume a streamline started from point r, on the surface and terminated at point r, at the end of the outlet (pipe). If the water speed emerging along the pipe does not depend on the size of the opening of the pipe or the cross-section of the pipe, find the speed of emerging water at the point r,, i.e., v, =? (Hint: use Bernoulli equation directly, do not assume its dependency on s)

Q: Can the distance traveled by a particle ever be less than its displacement? When are they equal?

A: No, the magnitude of the displacement is always less than or equal to the distance traveled.

Q: Prove that moments are independent of change of origin but not of scale.

A:

Q: x = X, +(-

A: let the initial velocity be v0 , and the initial distance be x0 .and in time t , the new velocity…

Q: 24) Find the maximum rate of change of at the given point and the direction in which it occurs.

A:

Q: A television camera is positioned 6 km from the base of a rocket launching pad. The rocket rises…

A: The television camera is positioned  from the rocketThe rocket is rising

Q: 4. What constant acceleration is required to increase the speed of a car from 30 mi/h to 50 mi/h in…

A:

Q: Rearrange the equation to isolate (a + b) (d_e) = f a

A: (a+bc)(d-e)=f(ac+bc)(d-e)=f

Q: reactangular field of 60 and 80m respectively two farmoers start moving from the same point and take…

A:

Q: s(t)%3D512 +t3 :-

A: Given information: st=5t2+t3 Find the velocity at -2.

Q: Two bicyclists begin a race at 8:00 a.m. They both finish the race 2 hours and 15 minutes later.…

A: Let f(x) and g(x) be the function of positions of these two bicyclists. Using the mean value…

Q: Explain how it can happen that an object with negative acceleration could speed up.

A:

Q: The projectile is thrown at the angle of 45 degrees with the initial velocity of 1 meter per second.…

A:

Q: When does the particle move at its greatest speed?

A: From the given graph it is clear that in the interval [1,2] v is negative and decreases also in this…

Q: Kratos kicks the ball with an initial speed of 70.0 m/s at an angle of 60.0º above the horizontal,…

A:

Q: Find the position and velocity of an object moving along a straight line with the given…

A:

Q: Watch the video and then solve the problem given below. Click here to watch the video. A flywheel…

A:

Q: Aservomotor controls the vertical movement of a drill bit that will drill a pattern of holes in…

A: Velocity graph is shown below:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.