A body of mass 10 slugs is dropped from a height of 1000 ft. with no initial velocity. The body encounters an air resistance proportional to its velocity. If the limiting velocity is known to be 320 ft./sec, find the time required for the body to attain a velocity of 160 ft./sec.

Q: A steel ball weighing 2 lb is dropped from a height of 3000 ft with no velocity. As it falls, the…

A: Locate the coordinate system with ground x = 3000 , w = 2lb  , k = 1/8 Assuming g is 32 ft/s W =…

Q: A tank initially holds 100 gallons of brine solution containing 20 lbs. of salt. At t = 0, fresh…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: There was a girl in a class studying math with, of course, a math teacher. This girl's name is…

A: Given query is to find the amount converted in two hours.

Q: Water is leaking out of an inverted conical tank at a rate of 12000.0 cm3/min at the same time that…

A: Given, Water is leaking at a rate of  12000 cm3/min Height of the tank is 9 m which is same as  900…

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 30 meter…

A: Mass of rope = 0.1kg/mMass of rope on bucket = 0.1kg/m*1m = .1kg…

Q: A spherical balloon is deflating and its radius r is decreasing at the rate of 5 mm per minute.…

A:

Q: Water is leaking out of an inverted conical tank at a rate of 10000.0 cm3/min at the same time that…

A: Given that, diameter is 5.5 m which is equivalent to 550 cm.. Therefore, radius is 5502=275 cm.…

Q: A ball is thrown vertically upward from the ground with an initial velocity of 115 ft/sec. Use…

A:

Q: 1. A person throws a ball upward from the top of a building 80 ft from the ground. What should be…

A: TO FIND: Initial velocity

Q: A 20 m tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: In this question, we find the amount of solt when the takl half full. given that  Initial amount of…

Q: A tank initially holds 1 cubic meter of a brine solution containing 20 kg of salt. Att= 0, fresh…

A:

Q: 6. The angle of elevation of the sun is decreasing ata rate of 0.15 rad/h. Hbw fast is the shadow…

A: From the given data:

Q: A body has initial velocity 20 m/s as it moves in a straight line with acceleration func- - m/s?.…

A: By using integration formula, we calculate the required values.

Q: Water is leaking out of an inverted conical tank at a rate of 11800.0 cm/min at the same time that…

A:

Q: A tank initially holds 410 liters of brine solution containing 7 kg of salt. At t=0, another brine…

A:

Q: A 100-gallon tank is full of a solution containing 20 pounds of a concentrate. Starting at time t =…

A:

Q: . A mass of 1 kg is attached to the end of a spring whose restoring force is 180 The mass is in a…

A:

Q: A brine solution of salt flows at a constant rate of 6 L/min into a large tank that initially held…

A: given, brine solution of salt flows at a constant rate of 6 Lmin the tank initially had 100 L of…

Q: Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always two…

A: The radius is 2 times the height, the rate at which the height increases is 3 cm/s when the pile is…

Q: A boat travels 100 miles upstream against a 10 mile/hour current. When the boat's velocity is v…

A:

Q: A ladder is slipping down a vertical wall. If the ladder is 13 ft long and the top of it is slipping…

A: Given ,dydt=-2ft/s     negative sign because as ladder is slipping down, y decreasesby Pythagor…

Q: 3. Using a powerful air gun, a steel ball is shot vertically upward from the ground with a velocity…

A: Newton's equations are to be used here

Q: A 100 L mixing tank initially contains 50 L of brine solution with 16 g/L concentration. Brine…

A: Let V be the volume of the tank. Thus, Vt=50+4+2-5t       =50tL where, t is the time in minutes.

Q: Suppose that a car starts from rest, its engine providing an acceleration of 10 ft/s², while air…

A:

Q: 8. An express train reducing its velocity to 40 km./h. , has to apply the brakes for 50 sec. . If…

A: Given that  Velocity of express train =40km/hr  Breaks apply at 50sec Retardation =0.5m/sec^2 To…

Q: A tank initially holds 1 cubic meter of a brine solution containing 20 kg of salt. Att = 0, fresh…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: ) A Cylinder tank of radius 4m and height 10m is initially filled with water. At the bottom of the…

A: Given that radius of a Cylinder tank is 4 meters and Height of tank is 10 meters. A hole is at the…

Q: A bucket that has a mass of 15 kg when filled with sand needs to be lifted to the top of a 25 meter…

A:

Q: Water is leaking out of an inverted conical tank at a rate of 6000.0 cm3/min at the same time that…

A: It is given that the height of the tank is h = 10.0 m and the diameter at the top is 6.0 m, that is,…

Q: Water is leaking out of an inverted conical tank at a rate of 6900 cubic centimeters per min at the…

A: Given,  water inflow = 6900 cm3/min. Height of the tank = 8 meters = 800 cm.  The radius of the top…

Q: 4) A particle is moving along the curve y = vx. As the particle passes through the point (4,2), its…

A:

Q: With what initial velocity must an object be thrown upward from a height of 8 feet to reach a…

A:

Q: A brine solution of salt flows at a constant rate of 7​L/min into a large tank that initially held…

A:

Q: High-speed train is to have a maximum speed of 450 km/h. Regulations require that the brakes must…

A: We will find the constant rate of deceleration qs following .

Q: 4. A solid cylindrical cord of elastic material has length 32 inches and radius 0.5 inch. The cord…

A: Given:        Length  l=32 inches        radius  r=0.5 inch      Volume of a cylinder  V=πr2l…

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 20 meter…

A: Given: Mass of bucket = 10kg Mass of the rope = 0.1kg/m Height of the Building = 20 meter

Q: The side of an equilateral triangle is increasing at a rate of 3 m/sec, then the rate at which its…

A: Let the side of an equilateral triangle be x cm.∴ Area of equilateral triangle, A = √3/4x2…

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 30 meter…

A: Given:    Mass of the bucket =10 kg   Mass of the rope =0.2 kg/m  Height of the building =30 m…

Q: 3. A flare is fired straight up from the ground with an initial velocity of 100 ft/s. How long will…

A: The position equation is given by: s=-16t2+v0t+s0 Where s is the final position, s0 is the initial…

Q: A triangle has a height that is increasing at a rate of 2 cm/sec and its area is increasing at a…

A:

Q: A bucket that has a mass of 15 kg when filled with sand needs to be lifted to the top of a 20 meter…

A: We are given that the mass of the bucket is 15 kg, the height of the building is 20 meter, the…

Q: A bucket that has a mass of 25 kg when filled with sand needs to be lifted to the top of a 25 meter…

A: If an object moves in a straight line by a continuous force, F(x), the work done by the force from…

Q: Water is leaking out of an inverted conical tank at a rate of 14000 cubic centimeters per min at the…

A: Given that, the leakage rate is 14000 cubic centimeter, the height of the tank is 12 meters and…

Q: 3. The period of free undamped oscillations of a mass on a spring is sec. If the spring constant is…

A: Given: We have to find: Numerical value of weight.

Q: Water is leaking out of an inverted conical tank at a rate of 9400.0 cubic centimeters per min at…

A: Explanation: Start by ignoring the leakage and determine the rate of inflow required to achieve the…

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 10 meter…

A:

Q: Water is leaking out of an inverted conical tank at a rate of 6900.0 cm/min at the same time that…

A:

Q: The rate of conversion of a certain substance is proportional to the square root of the amount m of…

A: We need to find time.

Q: 2. The maximum amount of solid waste collected per day for one week is presented below. All the…

A: Given The maximum amount of the solid waste collected per day for one week is presented below All…

Q: Water is flowing at constant rate of 120 cc/sec in a hemispherical bowl with radius 18 cm. If the…

A: ANSWER: Option a) 0.1669 cm/s

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.