A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attached to the front of the boat, which is 9 feet below the level of the pulley. If the rope is pulled through the pulley at a rate of 18 ft/min, at what rate will the boat be approaching the dock when 90 ft of rope is out?

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: From the Pythagorean theorem, BC2+AB2=AC2

Q: A trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at…

A:

Q: A kite is flying at a height of 40 ft. A boy is flying it so that it is moving horizontally at a…

A: Given: Kite is moving horizontally at a rate of 3 ft per sec. To determine: The rate at which the…

Q: A 5 ft long ladder rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Let's understand what's going on:

Q: A pulley having a diameter of 36 cm is turned by a belt that moves at the rate of 5 m/sec. How many…

A: In one revolution the pulley will rotate by an angle of 360°. Hence, the belt will cover a distance…

Q: A 3 lb bucket containing 20 lb of water is hanging at the end of a 20 ft rope that weighs 4 oz/ft.…

A: Given that, a 3 lb bucket containing 20 lb of water is hanging at the end of a 20 ft rope that…

Q: A 50 feet ladder is leaning against a wall of a building. Suppose the base of the ladder slides away…

A: Rate of change

Q: A rod of length 2m is connected at its ends to perpendicular sliders so that moving one end also…

A: Let y m be the height of the slider and x m be the foot of the rod away from the slider. Then,  by…

Q: A kite is 40 ft. high with 50 ft. of cord out. If the kite moves horizontally at 5 mi. per hr.…

A: Draw the position of kite as shown below.

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: We have  height of pulley =1 m rate of approach =1 m/s We can assume a triangle as Where x as base…

Q: A light is at the top of a 16 ft pole. A man 6 ft tall walks away from the pole at a rate of 5ftsec…

A:

Q: A trough is 14 ft long and its ends have the shape of isosceles triangles that are 5 ft across at…

A:

Q: A trough is 10 ft long and its ends have the shape of isoscelestriangles that are 3 ft across at the…

A:

Q: A woman is flying a kite on a long string. The kite itself has a 150 ft above the ground of the wind…

A: In the question we have to find the rate of string to let out.

Q: A boat is pulled into a dock by rope attached to it and passing through a pulley on the dock…

A: Calculus

Q: A boat is being pulled with a rope towards a dock that is 10 ft above the water, as shown in the…

A: Let the distance of the boat= x ft y=length of the rope.  So,  given that dy/dt= 1.5 ft/min We have…

Q: A ladder 13 feet long is leaning against the wall. If the base of the ladder is pushed toward the…

A:

Q: A triangular trough is 10ft long, 6 ft across the top, and 3 ft deep. If water flows in at the rate…

A: Given: A triangular trough is 10 ft. long, 6 ft. across, and 3 ft. deep.If water flows in at the…

Q: A kite 50 ft above the ground is moving horizontally at a rate of 4 ft/s. At what rate is the string…

A: We will be using the trigonometric ratios relating the sides of the triangle formed by strings and…

Q: The speed of a moving sidewalk at an airport is 2ft/sec. A person can walk 45ft forward on the…

A: Let his speed on a non-moving sidewalk is = x ft/sec Given the speed of the moving sidewalk = 2…

Q: A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is…

A: Given data:   The given height of the pulley is y=7 ft. The given rate at which rope pulled is…

Q: A boat is pulled toward a dock by means of a rope wound on a drum that is located 3 ft above the bow…

A: a rough sketch of the problem will be as follows:

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A:

Q: man 6 ft tall walks at a rate of 5 feet per second away from a light that is 15 ft above the ground.…

A:

Q: A ladder 10 feet long rests along a vertical wall. If the bottom of the ladder slides away from the…

A: To find the rate of change of the ladder's top changes with wall

Q: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its…

A:

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: Given : The pulley is 1 m higher than the bow The rate at which rope is pulled dydt=-1m/s and x=8.…

Q: A ladder is 36 feet long and is leaning against the side of a house. The base is moved away at 2 ft…

A:

Q: A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is…

A: Given

Q: A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away from her at…

A: Given A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away from…

Q: A light is on the top of a 12 ft tall pole and a 5 ft 6 in tall person is waking away from the pole…

A: Given that:Height of the poll is 12 ft and height of the person is 5 ft 6 in or 5.5 ft.Let x and y…

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: We sketch the situation roughly  Let us assume x=the distance of the boat from the dock y=the…

Q: A ladder 20 feet long is leaning against an embankment inclined 60 degrees to the horizontal. if the…

A: The ladder is leaning against an embankment inclined 60 degrees to the horizontal has length 20…

Q: The ends of a trough, 8 ft in length, are isosceles triangles with height 2ft and base 4ft. Water is…

A: Rate of change

Q: A rope is attached to the bow of a sailboat coming in for the evening. Assume that the rope is drawn…

A: Given: The rope is drawn in over a pulley 5 feet higher than the bow at the rate of 2 feet per…

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: Let A= Pulley , B= Boat Given that AC=1  Let, x= distance of the boat from the dock. y=length of the…

Q: A 35-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 8…

A: Let BC = x = distance from the base of wall to bottom of the ladderAB = y = distance from the base…

Q: A trough is 12 ft long and its ends have the shape of isosceles triangles that are 2 ft across at…

A: Given data:   The length of the trough is L=12 ft. The side of the isosceles triangle is b=2 ft. The…

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A:

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: The dock is 1m higher than the bow of the boat. Pulled rate of the rope of 1.4m/s To calculate the…

Q: A trough is 14 ft long and its ends have the shape of isosceles triangles that are 4 ft across at…

A: Given that: A trough is 14 feet long and its ends have the shape of isosceles triangles that are 4…

Q: A car braked with a constant deceleration of 16 fts 2 , producing skid marks measuring 200 ft…

A: Given, deceleration a(t) = 16 ft/sec2. s(0) = 0 ft and s(T) = 200 ft and v(T) = 0. Where T is the…

Q: A 15-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 3…

A:

Q: Suppose that the hot-air balloon was descending at a rate of 12 ft/sec instead of ascending.…

A:

Q: A trough is 12 ft long and its ends have the shape of isosceles triangles that are 2 ft across at…

A: Let the volume of the water in the trough at time be V. The rate of change of V is,

Q: A boat is pulled toward a pier by means of a taut cable. If the boat is 20 ft below the level of the…

A:

Q: light is 25 ft above a sidewalk and a man 6 ft tall is walking away from the point under the light.…

A:

Q: A 20-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 6…

A: Let x= horizontal distance y=vertical distance Given that dx/dt=6 ft/sec and x=16 ft At x=16 we find…

Q: A trough is 10 ft long and its ends have the shape of isosceles triangles that are 4 ft across at…

A: Let V be the volume of the water inside the trough and h be the height of the water inside the…

Q: A balloon ascending at the rate of 12 ft/sec is at a height 80 ft above the ground when a package is…

A: Sol:-v0=12 ft/secHeight = h = 80 ftThen, y-y0=v0t-12gt2