A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast (in m/s) is the length of his shadow on the building decreasing when he is 4 m from the building?

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: The sides of a square are increasing at the rate of 2 inches per minute. How fast is the Area…

A: Given The side of square is increasing at rate of 2inches per minute.  The area of a square with…

Q: A man 6 ft tall is walking toward a building at the rate of 5 ft/s. There is a light on the ground…

A:

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A: Given:    Distance = 250 meter per hour

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Q: A small balloon is released at a point 60 feet away from an observer, who is on level ground. If the…

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Q: A street light is fastened to the top of a 15-ft-high pole. If a 5-ft-tall women walks away from the…

A: In the figure,  AB=15 ft DE=5 ft BD=yDC=xdydt=3 ft/sec

Q: Two cars start moving from the same point. One travels south at 60 km/h and the other travels west…

A: follow next step

Q: A plane is flying at a constant altitude of 1 mile and a speed of 400 mph toward an observer on the…

A: The plane is flying at a constant altitude of 1 mile. Let x be the horizontal distance and y be the…

Q: The top of a 10 ft ladder slides down a vertical wall at a rate of 1 ft/sec. How fast is the…

A:

Q: A spotlight on the ground shines on a wall 12 m away. If a girl 1.2 m tall walks from the spotlight…

A:

Q: The top of a ladder 30 meters long leans against a vertical wall, and the lower end rests on a level…

A: Let the height of wall corresponding to the ladder lean at any instant be denoted as h. Let the…

Q: A weight is attached to one end of a 33-foot rope which passes over a pulley 18 feet above the…

A: The above problem statement can be pictorially represented as:

Q: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

A: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

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

A:

Q: A 5-foot-tall woman walks at 8 ft>s toward a streetlight that is 20 ft above the ground. What is…

A:

Q: An aircraft is flying horizontally at a speed of 600 km/h. How fast is the distance between the…

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: A 6-ft-diameter cylindrical tank is filled with water to a height of 10 ft. It is drained such that…

A:

Q: a man 5 ft tall is walking along a straight line at a rate of 3 ft/sec towardss a lamp post that is…

A: To find: The rate of the man shadow moving when he is 30 feet from the post. Given: The height of…

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: Shan, who is 2 meters tall, is approaching a post that holds a lamp 6 meters above the ground. If he…

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

A: Let, a be the spotlight and “ed” be the wall on which the spotlight shines.Therefore, “ad” is the…

Q: Two runners start moving from the same point. One runs north at 8 km/hr and the other runs east at…

A: • Distance travelled = Speed × time • The rate of change of the distance between the two runners can…

Q: Two runners start moving from the same point. One runs north at 8 km/hr and the other runs east at 6…

A: Pythagoras Theorem states that the square of the hypotenuse is equal to the sum of the squares of…

Q: A man 6 ft tall walks along a level sidewalk away from a lamppost. On the post is a street light 18…

A:

Q: A plane is flying at a constant altitude of 1 mile and a speed of 400 mph toward an observer on the…

A:

Q: A 3-m long steel pipe has its upper end leaning against a vertical wall and the  lower end on a…

A: Given that: Length of steel pipe=3mLower end moves away from the wall at a speed = 2cm/s

Q: A 13-foot ladder is resting against a wall and the bottom is initially 10 feet away from the wall.…

A:

Q: A lady 1.65 meters tall walks towards a lamp post 2.65 meters high at a speed of 1.5 m/s. How fast…

A: Given: Height of lady=1.65 m Height of lamp post=2.65 m Speed of lady=1.5 m/s To find: Shadow of…

Q: The base of a triangle begins to increase at a rate of 2 inches per minute while the height remains…

A: Consider the following variables, b=base of the triangleh=height of the triangleA=area of the…

Q: The base of a 13 foot ladder that is leaning against a wall begins to slide away from the wa When…

A: It is given that, length of the ladder x = 13 feet,  The distance between the foot of the ladder and…

Q: A man 2 m tall walks toward a lamppost on level ground at a rate of 0.5 m/s. If the lamp is 5 m high…

A:

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

A:

Q: A conical reservoir is losing water at the rate of 12 cubic feet per minute. If the radius is % the…

A: Let the height of the conical reservoir be h. Then the radius will be = h/4 Therefore we get the…

Q: A 6​-foot-tall woman walks at 9 ft/s toward a street light that is 24 ft above the ground. What is…

A: The height of the woman is 6 ft. and the height of the street light is 24 ft.The woman walks at 9…

Q: A spotlight on the ground shines on a wall 10 m away. If a man 3 m tall walks from the spotlight…

A:

Q: A man 6-ft tall walks with a speed of 5 ft./sec. away from a street light that is a top of a 24-ft…

A:

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

A:

Q: A man that is 5 feet tall is walking in a straight line at a rate of 3 ft / s towards a lamp post…

A:

Q: A 30-foot ladder is leaned up against a 2-story building with 8-foot floors. The bottom of the…

A: Consider the diagram below with marked information: Speed of change in base is 6 feet per second.

Q: A man 6 ft. tall is walking towards a building at the rate of 4 ft./sec. If there is a light on the…

A:

Q: A man 5 ft tall is walking along a straight line at a rate of 3 ft/sec towards a lamp post that is…

A: According to the given question,

Q: A man that is 6 feet tall walks towards a light that is 20 feet above the ground at a rate of 5 feet…

A: Given:      Height of man =6 feet     Height of light =20 feet     Rate of walk by man dxdt=5 ft/sec…

Q: A 22-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A: Leader is leaning against wall at AC=22 ft. Distance of the ladder from the wall is x=15 ft. Let the…

Q: The base of a 20-foot ladder is sliding toward a wall at a rate of 1.5 feet per second. How fast is…

A: We solve the above problem.