A tank in the form of a right circular cylinder standing on end is leaking water through a circular hole in its bottom. When friction and contraction of water at the hole are ignored, the height hof water in the tank is described by dh An V2gh, dt where A, and A, are the cross-sectional areas of the water and the hole, respectively. (a) Solve the DE if the initial height of the water is H. By hand, sketch the graph of h(t) and give its interval / of definition in terms of the symbols A, A, and H. Use g = 32 ft/s?. (b) Suppose the tank is 10 feet high and has radius 2 feet and the circular hole has radius 1/2 inch. If the tank is initially full, how long will it take to empty?

Q: On a frozen pond, 10-kg sled is given a kick that imparts to it an initial speed of 2.0 m/s. The…

A: Initial kinetic energy is Final kinetic energy is

Q: A tank in the form of a right-circular cylinder standing on end (Figure 6.1) is leaking v through a…

A:

Q: A spring with constant k = 5 N/m hanging from the ceiling is placed at its lower end with an object…

A:

Q: 4. ( A 2-kg mass is attached to a spring with stiffness k = 18. Neglecting dampıng. write out the…

A: Given that: Mass of the attachment, m = 2-kg Stiffness of spring, k = 18 To find the equation of…

Q: A 5-g coin is dropped from a 300-m building. If it reaches a terminal velocity of 45 m/s, and the…

A: Given Weight of the coin =5×10-3kg The initial velocity of the coin =0 The final velocity of the…

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A:

Q: A spring is such that a 2-lb weight stretches it 6 in. There is a damping force present, with…

A: Given: The stretch of weight is 2 lb to 6 in The impressed force is 2 sin 8t

Q: A uniform sphere of mass m rolls from rest at A along a frictionless hemispherical surface, under…

A: Consider the given figure as

Q: 2. A Ferris wheel of diameter 18.5 m rotates at a rate of 9.2 rad/s. If passengers board the lowest…

A:

Q: 3. A tiny organism begins to move in a straight line with velocity v(t) = t(t – 1)'/3 microns per…

A: Let the expression for the velocity is v(t)=t(t2-1)1/3. Integrate the expression to find the…

Q: A mass weighing l16 pounds stretches a spring feet. The mass is initially released from rest from a…

A: Formula: Let m be the mass attached, k be the spring constant and β be the positive damping constant…

Q: An object with an initial velocity of v(0) = 5 has an acceleration of a(t) = t² - 5. What is its…

A: Concept: The acceleration is given by the derivative of the velocity  That is a(t)=dv(t)dt Thus…

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Given that: The height of the tank is 20 feet, radius is 8 feet and the radius of the circular hole…

Q: A bug is moving along the right side of the parabola y =x at a rate such that its distance from the…

A:

Q: 6) A weight oscillates in a vertical motion according to the position function y(f) = -5 cos t.…

A: Acceleration for position function yt=-5cost is d2ydt2. Calculate double derivative d2ydt2 and…

Q: After a mass weighing 10 pounds is attached to a 5-foot spring, the spring measures 7 feet. This…

A: Let m be the mass , k be spring constant and  β be positive damping constant. The Newton's second…

Q: A 5 kg weight is attached to a spring with constant k = 80 N/m and subjected to an external force…

A: Consider my¨+ky=Ft......1 Given that m=5 kg, k=80 Nm and Ft=140sin3t..…

Q: A cylindrical tank as shown in Figure Q 1 is initially filled with water to a height, ho (m). The…

A: Solution:

Q: The Debroglie wavelength of an electron * .with a velocity of 1.00x 10^6 m s-1 mass of electron is…

A: Debrogile wavelength:

Q: The tank in the form of a right-circular cone of radius 11 feet and height 15 feet standing on its…

A: Given: Let us consider the right-circular cone, Radius=11 feet Height=15 feet and circular hole of…

Q: An object with mass m is attached to a spring with spring constant 1 N/m. If the mass is pulled Im…

A:

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in…

A: A detailed solution is given below.

Q: (b) (i) The measurement of the edge of a cube is found to be 15 inches, with a possible error 0.03…

A:

Q: On a different planet, an object is thrown straight upward at an initial speed of 13 m/s and its…

A: We have to integrate the given acceleration function to find the velocity function.  At max. height,…

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A:

Q: (9) (a) In this question use a(t) = -32 feet / sec? as the acceleration due to gravity. S(1) =gt gt²…

A:

Q: A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the…

A: given,

Q: A skydiver’s vertical velocity is governed by m(dv/dt)=mg-k(V^2) where, ? is the mass of the…

A:

Q: A 0.500 kg block is traveling at 4.00 s when it collides with a 3.50 kg ball at rest. Following the…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: The displacement of a structure is defined by the following equation for a damped oscillation y =…

A: By this method 1st we will find an interval where roots can lie and then use xn+1=xn-f'(xn)f(xn) to…

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find da/dt in…

A: Given that  Area of the circle =A  Radius of the circle =r  To find the rate of change of area

Q: A 3 kg mass is attached to a spring with stiffness k = 48N / m. The mass moves 1/2 m to the left of…

A: The equation can be given as; y" + (k/m)y =0,   The mass moves 1/2 m to the left of the equilibrium…

Q: An 80-lb weight is attached to the lower end of a coil spring suspended from the ceiling and having…

A: We have given that the spring constant (k)=62.6 lb/ft, weight =80 lb and mass=8032=2.5 lb s2/ft We…

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A:

Q: Collars A and B of same mass m are moving towards each other with velocities shown in Fig. Ex.…

A: Solution:

Q: Suppose water is leaking from a tank through a circular hole of area An at its bottom. When water…

A:

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Given: Let us consider the given, dhdt=-56h32 c=0.6, g=32 ft/s2 Vertex angle=60°

Q: A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of…

A: The Solution is given below

Q: in terms of dt dt (a) If A is the area of a circle with radius r and the circle expands as time…

A:

Q: A tank in the shape of a cylinder standing on end leaks water through a circular hole in its bottom.…

A:

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A:

Q: A 0.5 kg mass is attached to a spring having a spring constant of 8 N/m. The mass is set into motion…

A:

Q: "The tank in the form of a right-circular cone of radius 16 feet and height 40 feet standing on its…

A: given that a tank is in the form of a right circular cylinder of radius 16 feet and height 40 feet…

Q: After a mass weighing 10 lbs. is attached to a 5 ft. spring, the spring measures 7 ft. This mass is…

A: Here is the Answer and Explanation

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A:

Q: the lengths a, b, and c of the edges of a rectangular box are changing with time. at the instant in…

A: Given:  a = 1m, b = 2 m, c = 3 m, da/dt = db/dt = 1 m/sec, and dc/dt = -3 m/sec

Q: Assume the motion of a mass-spring system with damping is governed by d²x dx +b 1 +16x = 0; x(0)=;,…

A:

Q: A cylindrical tank of height 13 metres is full of water at time t = 0 seconds. is turned on at the…

A:

Q: A mass weighing 8 lb stretches a spring 3 in. The mass is attached to a viscous damper with a…

A: