Suppose you always keep your eyes fixed on the very top of a 100 m building. Suppose you start to run towards the building at a rate of 5 m/s. How quickly is the angle of your head changing when you are 75 m from the base of the building?

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:

Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

A: Let y be height of wall upto ladder and x be distance between bottom of wall and bottom of ladder…

Q: A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A: A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

Q: In an isosceles right triangle, the hypotenuse is increasing at a rate of 0.1 ft/s. When the area of…

A:

Q: A hot-air balloon is 150 ft above the ground when a motorcycle (traveling in a straight line on a…

A: Let x be the distance the motorcycle has traveled. Let y be the height of the balloon above the…

Q: A 5 foot girl is walking toward a 20-foot lamppost at the rate of 6 feet per second. How fast is the…

A:

Q: A 6-ft tall man is walking away from a 15-ft tall street lamp at the rate of 5 ft/sec. How fast is…

A: Here we find rate of shadow lengthening.

Q: A ladder 15 ft long leans against a vertical wall. If the top slides down at the rate of 2 ft per…

A:

Q: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how…

A: Given: Since the height is decreasing.     To determine:

Q: The sides of a square decrease in length at a rate of 1 m/s. At what rate is the area of the square…

A:

Q: the altitude of a triangle increases at a rate of 1 cm/min while its area increases at a rate of 3…

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 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 ladder 20 feet long leans against a house. What is the rate at the top of a ladder that is moving…

A: Given that ,      A ladder 20 feet long leans against a house. We have to calculate the rate at the…

Q: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A: First I have draw the graph of given problem and then solved them using Pythagoras theorem. The foot…

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

A:

Q: A baseball diamond has the shape of a square with sides 90 feet long, suppose the player is running…

A: It is given that a baseball diamond has the shape of square with side 90 feet long. Construct the…

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

A: Given thatLadder length = 10 ftDistance of ladder from the bottom of wall = 6 ftRate of change of…

Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

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 man drives at a rate of 25 kph towards the foot of an 8-m tall monument. At what rate is he…

A: Topic = Algebra

Q: A man of 2 mts tall is approaching a lamp post at the rate of 0.5m/sec.if the lamp post is situated…

A:

Q: A man of height 1.7meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate at…

A: Given that a man of height 1.7m walks away from a 5 meters lamp post at a speed of 1.1 m/s. We need…

Q: The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the rate…

A: Given that  The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute.…

Q: A ball is dropped down a well and 5 sec later the sound of the splash is heard. If the velocity of…

A: The complete solutions are given below

Q: A flying kite is 100 m above the ground, moving in a horizontal direction at a rate of 10 m/s. How…

A:

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

A:

Q: A 17 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how…

A:

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

A: Definition uses-       Similar triangles -        If two triangles are similar then their…

Q: A 13-ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A:

Q: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A: Let x be the distance between wall and bottom of ladder and y be the distance of top of ladder from…

Q: A 6-ft tall man is walking towards a 15-ft tall street lamp at the rate of 9 ft/sec. How fast is his…

A:

Q: Two cars start moving from the same point. One travels south at 84 mi/h and the other travels west…

A:

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

A:

Q: A searchlight, 1/2 mi from a straight shore, rotates at the rate of 2 rev/min. How fast is the spot…

A: Let the angle formed by line AB with the line AC is x  in the triangle ABC,   So, from the tangent…

Q: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how…

A: A 13 feet ladder is leaning against the wall. The top slips down the wall at a rate of 2 ft/s. The…

Q: . A 6-ft tall man is walking away from a 15-ft tall street lamp at the rate of 5 ft/sec. How fast is…

A:

Q: A 15 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A:

Q: A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At which rate is the angle…

A: Given,  Consider the height of the lite from the ground is 100 ft. The speed is dxdt=8 ft/s. To find…

Q: A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how…

A: Firstly we will draw the diagram for given information and then find the required as shown below

Q: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A:

Q: A 15 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A:

Q: Two cars start moving from the same point. One travels south at 64 mi/h and the other travels west…

A:

Q: A tubular metal 3.9 meters long leans against a vertical wall and the other foot of the metal is on…

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 light is placed on the ground 30 ft from a building. A man 6 ft tall walks from the light toward…

A: This question is based on application of derivative.

Q: A ladder 13 meters long is leaning against a wall. If the bottom of the ladder is being pushed…

A: