A ship moving 8 mph sails north for 30 minutes then turns east. If a searchlight at the point of departure follows the ship, how fast is the light rotating 2 hours after the start?

Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

A: Given  Speed of first car =48 mi/h towards south Speed of second car =20 mi/h towards west

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

A:

Q: A neighborhood carnival has a merrygo-round whose radius is 25 feet.If the time for one revolution…

A: Since,it is known that the speed can be calculated by using the formula speed=Radius×Angular…

Q: At noon, ship A is 150 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing…

A:

Q: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

A: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

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: At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing…

A: distance between the ship A and B is 150 km speed of ship A is 35km/h so at time t, the distance…

Q: A 4.5 ft tall man is walking away from a 25 ft tall lamp post.  If he is walking at a rate of 2…

A:

Q: A commercial airplane flying with a speed of 700 mi/h is detected 1000 miles away with a radar. Half…

A: Given:

Q: A man 6 feet tall walks at a rate of 4 feet per second away from a light that is 15 feet above the…

A: Please see the explanation below

Q: A spotlight on the ground shines on a wall 12m away. If a man 2m tall walks from the spotlight…

A:

Q: One speed skater starts across a frozen lake at an average speed of 9 m/s. Ten seconds later, a…

A: Let t= time in second d=distance Also, consider second skater time in second is t .

Q: A helicopter flies parallel to the ground at an altitude of 1/2 kilometer and at a speed of 2…

A:

Q: A man 7 ft tall walks at a speed of 5 ft/sec toward a street lamp which is 15 ft above the ground.…

A:

Q: At noon, ship A is sailing north at a speed of 7mph, at the same time ship B, 5 miles west of ship…

A: Given, at noon, Ship A is sailing north at a speed of 7mph. At the same time, Ship B, which is 5…

Q: A 17 feet ladder is leaning against a wall. if the bottom of the ladder is pulled along the ground…

A: Given:- A 17 feet ladder is leaning against a wall. if the bottom of the ladder is pulled along the…

Q: One car leaves a given point and travel north at 30 mph. Another car leaves 1 hour later, and travel…

A:

Q: A spotlight on the ground is shining on a wall 24m away. If a woman 2m tall walks from the spotlight…

A: Here we use the application of derivative

Q: A spotlight on the ground shines on a wall of a building 20 feet away. If a man 6ft tall walks from…

A:

Q: Two people start from the same point. One walks east at 2 km/h and the other walks northeast at 3…

A:

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

A:

Q: A lighthouse is located on a small island 3km away from the nearest point P on a straight shoreline…

A:

Q: Two people start from the same point. One walks east at 2km/h and the other walks northeast at 3…

A: Given

Q: A van starts off 152 miles directly north from the city of Springfield. It travels due east at a…

A: The distance between the van and the city of Springfield is 152 miles in the north direction. The…

Q: A street light is at the top of a 13 foot tall pole. A 6 foot tall woman walks away from the pole…

A: The given data is: A street light is at the top of a 13-foot tall pole A 6-foot tall woman walks…

Q: There are 100 bacteria cells in a dish now, but in 5 hours there will be 147 cells. At what rate do…

A: There are 100 bacteria at initial time t=0. In 5 hours that is when t=5, there will be 147 cells. In…

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 feet tall walks away from the…

A:

Q: One speed skater starts across a frozen lake at an average speed of 9 m/s. Ten seconds later, a…

A:

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 feet tall walks away from the…

A:

Q: A lighthouse, L, is on an island 8 mi away from the closest point, P, on the beach. If the…

A: Given: A lighthouse rotates clockwise at a constant rate of 17 revolutions/min.

Q: A girl starting at 11 A.M., travels east at 4 km/hr while a boy, starting at noon from the same…

A:

Q: A lighthouse, L, is on an island 4 mi away from the closest point, P, on the beach. If the…

A:

Q: The fixed sides of an isosceles triangle are of length 6 cm. (See the figure.) If the sides slide…

A: Given: The fixed sides of an isosceles triangle are of length 6 cm and the sides slide outward at a…

Q: Two cyclists, 90 mi apart, start riding toward each other at the same time. One cycles twice as fast…

A: Given that, the distance between two cyclists is 90 mi, and one cycles twice as fast as the other…

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 feet tall walks away from the…

A: Diagram of the given question will be as following x is the distance of the man from pole y is the…

Q: One car leaves a given point and travels north at 30 mph. Another car leaves1 hour later, and…

A:

Q: One car leaves a given point and travels north at 40 mph. Another car leaves 1 HOUR LATER, and…

A: Let's find rate of change distance between the cars changing at the instant the second car has been…

Q: A computerized spin balance machine rotates a 25-inch-diameter tire at 480 revolutions per minute.…

A:

Q: A man 6 feet tall walks at a rate of 3 feet per second away from a light that is 15 feet above the…

A:

Q: A man 6 feet tall walks at a rate of 7 feet per second away from a light that is 15 feet above the…

A: Let OA= height of light      CD= height of man      BC= length of shadow…

Q: was an earthquake in South America with magnitude 4.3 that caused only minor damage. How many times…

A:

Q: A lighthouse is on a small island 4 km from the nearest point P on a straight shoreline. Its beacon…

A: Given: lighthouse is situated on a small island 4 km from point P   number of revolutions= 1…

Q: A man, running 3 meters per second in an open field, runs east for 30 seconds, then turns north.  If…

A: Since the man ran 3m/s east for 90 sec so he is 90 m from the searchlight. Consider the diagram…

Q: A revolving beacon is situated 3600 feet off a straight shore. If the beacon turns at 2 revolutions…

A:

Q: A lighthouse is located on a small island 3 km away fromthe nearest point P on a straight shoreline…

A:

Q: A hot air balloon is tethered at an angle of elevation of a/6. The rope holding the balloon is being…

A: Given Data: The angle of elevation is: α=π6 The rate at which the rope is being brought is: dxdt=-4…

Q: One car leaves a given point and travels north at 30 mph. Another car leaves 1 hour later, and…

A: Assuming that car are travelling along the y-axis and x-axis respectively.The position of cars is…