A hot-air balloon is rising vertically at a rate of 5 meters/sec. An observer stands 300 meters from where the balloon left the ground. At what rate is the distance between the observer and the hot-air balloon changing at the moment the balloon is 50 meters high?

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

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Q: Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west…

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Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: Let the ladder is k meters. (k=constant) Let the distance of the bottom = x m and distance of the…

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

A: To find- rate at which its top moving up the wall.

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 man whose height is 1.5 m. is walking directly away from a lamp post at a constant rate of 0.8…

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Q: A 10-metre ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away…

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Q: A 5-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away…

A: To find the rate of change of area of the triangle formed .

Q: An arc light is hung 12 ft. directly above a straight horizontal wall on which a boy 5 ft. tall is…

A: Given an arc light is hung 12 ft. directly above a straight horizontal wall on which a boy 5 ft.…

Q: A spherical balloon is inflated with gas at a rate of 10 cubic metres per minute. How fast is the…

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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: A baseball diamond is a square with side 90ft. A batter runs toward first base at 25 feet per…

A: Assume x = distance batter has run at time t andD = distance from second base to the batter attime…

Q: A balloon is rising vertically over a point A on the ground at the rate of 15 ft/sec. A point B on…

A: Let the distance of the balloon from point B be denoted as p. The balloon, points A and B form a…

Q: A sphere is filled with air. If the volume of the sphere is decreasing at a rate of 534 cubic cm per…

A: Given

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 1.8 m walks away from a 5-m lamppost at the speed of 1.2 m/s. Find the rate at which…

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Q: The lower base of a trapezoid is 8 m. If its height is increasing at the rate of 0.5m/sec while its…

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

A: Given the data :

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

A:

Q: A weather balloon is rising vertically at the rate of 10 ft/s. An observer is standing on the ground…

A: Given:A weather balloon is rising vertically at the rate of 10 ft/s. An observer is standing on the…

Q: A 5​-foot-tall woman walks at 4ft/s toward a street light that is 25ft above the ground. What is the…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.125 m/s. At the moment when the…

A: To find: -

Q: A man 2m tall is walking at the rate of 2m/s away from a lamp post 7m high. At what rate is the tip…

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 12-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

A: A 12-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

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

A: Consider the provided information, Let x and y be the traveled by the cars after time t. We can…

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 spherical balloon is inflated at a rate of 10 cm3>min. At what rate is the diameter of the…

A:

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 spherical balloon is filled with gas at a rate of 300 mm3/sec. Find the rate at which the surface…

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Q: The rate at which bacteria multiply is proportional to the instantaneous Number Present. If the…

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

A:

Q: A cone-shaped tank of water is leaking water at a constant rate of 2 m3/hour. If the base radius of…

A: Given that

Q: The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the bottom…

A: Given,

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

A:

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

A:

Q: At what rate is the height of the water rising at the instant the tank is half full?

A: To find the rate at water rising

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

A: Let x= horizontal distance L= length of string,  Then a rough sketch of the problem is as follows:

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 small balloon is released at a point 150 feet away from an observer who is on level ground. If the…

A: we have to find

Q: How fast is the tip of her shadow moving?

A: Concept:   The calculus helps in understanding the changes between values that are related by 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 baseball diamond is a square with side 90ft. A batter hits the ball and runs toward first base…

A:

Q: The area of a rectangle is increasing at a rate of 4 cm/sec ? while the width of the rectangle…

A: The area of a rectangle is increasing at a rate of 4 cm/sec ? while the width of the rectangle…

Q: A weather balloon is rising vertically at the rate of 10ft/s. An observer is standing on the ground…

A: Given: -

Q: Two cars start moving from the same point. One travels south at 56 mi/h and the other travels west…

A:

Q: Two cars start moving from the same point. One travels south at 16 mi/h and the other travels west…

A: A goes to south at 16 mi/h, so dA/dt= 16  After 3 hours A will be 16*3=48 mi away from the origin.…

Q: A 15-foot ladder is slider down a wall at a rate of 3 ft/sec.  At what rate is the bottom of the…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.25 m/s. At the moment when the bottom…

A: Let the height up of the wall to the top of the ladder is y. let the distance between the bottom of…