Two boats leave a port at the same time: one travels west at 20 mi/hr and the other travels south at 15 mi/hr. a) After 30 minutes how far is each boat from port? b) At what rate is the distance between the boats changing 30 minutes after they leave the port?

Q: (b) If its' owner uses 3 pipes of radius 4cm, with water flowing at a rate of 30cm/s, how long will…

A: (a) Area of circuler face= pi*r2  =pi*102 = 314 cm2.                    (pi=3.14)

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: each side of a square increases at a rate of 1.5cm/sec .also find the rate at which the area of the…

A: Given,   Each side of a square increases at a rate of 1.5 cm/sec

Q: A baseball is thrown straight downward with an initial speed of 40 ft/s from the top of the…

A: Let t be the time taken by the ball to reach the ground and the velocity of the ball is v. Now, the…

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 ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Given: Length of a ladder which rests against a vertical wall is 10 ft. Let the distance between…

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 kite 160 feet above the ground moves in a direction parallel to the ground at the rate of 5 feet…

A: Let, x= the horizontal distance of the kite y=the length of the string Given that dx/dt=5 ft/sec  We…

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

A: To find: The rate at which the angle between the ladder and the ground  is changing

Q: A train 220 m long is running with a speed of 59 kmph . In what time wil it pass a man who is…

A:

Q: A kite 30 m above the ground moves horizontally at a speed of 10 m/min. At what rate is the angle…

A:

Q: A 6 ft tall Batman runs (into the night) away from a 10 ft streetlamp at a rate of 1 How fast is his…

A:

Q: A ladder 25 ft long is leaning against a wall. If the bottom of the ladder is pulled 10.…

A: We need to find change in angle.

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

A: In the figure, x is the distance of pole from the man at the ground level. s is the length of the…

Q: When a rocket is 2 kilometers high, it is moving vertically upward at a speed of 300 kilometers per…

A:

Q: An 8 ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall…

A:

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

A: →cosθ = BaseHypotenuse→sinθ = 1-cos2θ→dcosθdθ = -sinθ

Q: A train, starting at noon, travels north at 40 ml per hr. Another train, starting from the same…

A:

Q: A ladder 40.2 ft long is leaning against an embankment inclined 70.4° to the horizontal. If the…

A:

Q: A snail slid 7 cm down a stalk and climbed 5 cm back up. Hlow far was the snail below its original…

A: Given : A snail moves 7 cm down then moves 5 cm up.

Q: A fish is reeled in at a rate of 1 foot per second from a bridge 15 ft. above the water. At what…

A:

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

A: Given  Height of the man =6ft  A street light is mounted at the top of a 15-ft-tall pole Let the…

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

A:

Q: the tires of a bicycle have a radius of 14inches and are turning at the rate of 230 revolutions per…

A: Given that the tires of a bicycle have a radius of 14inches and are turning at the rate of 230…

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

A: Please refer the attached image for complete solution. THANK YOU !

Q: When a rocket is 3 kilometers high, it is moving vertically upward at a speed of 400 kilometers per…

A: Let the height of the rocket be h and the angle of elevation from the observer’s eye is x.

Q: 2. A steel girder 27 feet long is to be moved on rollers along a passageway 8 feet in width and into…

A: Given: A steel girder 27 feet long is to be moved on rollers along a passageway 8 feet in width and…

Q: An 8 ft. ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall…

A:

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 kite is flying at a fixed height of 30 ft. If 50 feet of stringis out alreadyfrom the spool, what…

A: Given: A kite is flying at a fixed height of 30 ft. If 50 feet of string is out already from the…

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

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

Q: A ball is thrown at an downward angle of 36.3 deg. from the horizontal at 43.4 m/s from a height of…

A: Explanation: Given that,  h = 36.9 m Downward angle: θ=36.3° vo=43.4 m/s   Concept Used: Horizontal…

Q: Two people start from the same point. One walks east at3 mih and the other walks northeast at 2 mih.…

A: Given dcdt=3mi/hdbdt=2mi/ht=15min=1560=0.25hr

Q: At noon,ship a is 130 km west of ship b.Ship a is sailing east at 25 km/h and ship b is sailing…

A:

Q: When a rocket is 3 kilometers high, it is moving vertically upward at a speed of 400 kilometers per…

A:

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

A: To determine the rate of change of angle between the ladder and the ground.

Q: An aircraft is climbing at a 300 angle to the horizontal. How fast is the aircraft gaining altitude…

A: An aircraft is climbing at a constant 30 degree angle to the horizontal and the speed is 500 mph…

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

A:

Q: A baseball diamond has equal sides of 90ft in length and each pair of adjacent sides are…

A:

Q: 5. must the ball be launched to land 450 ft from the base of the building? A golf ball is hit in a…

A:

Q: Two people start from the same point. One walks east at3 mi/h and the other walks northeast at 2…

A:

Q: Car A is traveling west at 50 mih and car B is traveling north at60 mih. Both are headed for the…

A: Since, we have been given that Car A is travelling west at 50 mi/hand Car B is travelling north at…

Q: Two people on bikes are separated by 350 meters. Person A starts riding north at a rate of 8 m/sec…

A:

Q: A train traveling up in inclined of 4° travels a horizontal distance of 4 km. how much altitude has…

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

A:

Q: A baseball diamond has the shape of a square with sides 90 feet long.  Suppose that player A is the…

A: Use Pythagoras theorem

Q: A ladder 9 ft long rests agains a vertical wall. If the bottom of the ladder slides away from the…

A: Let the distance between base B of the wall and bottom of the ladder C, BC= x feet  And the angle…

Q: Suppose that you just completed a nonstop bicycle trip of 5.5 km. You know that each wheel of your…

A: Given Data: The distance covered by the bicycle is: d=5.5 km=5500 m The radius of the wheels of a…