A helicopter blade spins at exactly 95 revolutions per minute. Its tip is 3.00 m from the center of rotation. (a) Calculate the average speed (in m/s) of the blade tip in the helicopter's frame of reference. m/s (b) What is its average velocity (in m/s) over one revolution? m/s

Q: A spherical snowball melts at a rate of 36π^2in³/sec. At what rate is the radius of the snowball…

A:

Q: A rocket is fired vertically upward from the ground with an initial velocity of 580 ft / sec. How…

A: Given : Initial velocity = 580 ft/sec

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

A: The diagram of the situation is shown below:

Q: Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section…

A: The situation is as shown below: Consider a small differential element of water at a height of h…

Q: Water is poured into a conical paper cup at the rate of 3/2 in/sec (similar to Example 4 in Section…

A: I will use the formula V=13πr2h and differentiation method to solve this problem.

Q: 3. A spherical balloon is inflated at a rate of 100 cm3 /sec. How fast is the radius changing when…

A: We know that volume of the balloon is V=43πr3                          (1) Given that Spherical…

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 spherical balloon is inflated with air at a rate of 32 cm3/ min. At what rate does the radius…

A: Find dr/dr.

Q: Find the rate at which the surface area of the water changes when the water is 10 ft high if the…

A:

Q: 1. A 15-meter ladder is resting against a vertical wall. If the bottom of the ladder is being pushed…

A: given: A 15-meter ladder is resting against a vertical wall. the bottom of the ladder is being…

Q: The radius of a spherical balloon is decreasing at a rate of in/sec.

A: Radius of balloon = r = 4 inchesDecreasing rate of balloon = drdt = -2πinches/secondVolume of…

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

A:

Q: A kite 100 feet above the ground moves horizontally at a speed of 10ft/s. At what rate is the angle…

A: Let the horizontal distance be x. From the given data of question: And the diagram is:

Q: Can instantaneous velocity be defined as a ratio? If not, how is instantaneous velocity computed?

A: We know that instantaneous velocity is the average velocity between two points on the path in the…

Q: Fireworks are fired up from a platform 3 ft. above the ground with an initial velocity of 125 ft/s.…

A: Given that: Fireworks are fired up from a platform 3 ft. above the ground with an initial velocity…

Q: A stone is dropped from the edge of a roof, and hits the ground with a velocity of -120 feet per…

A:

Q: A 15-meter ladder is resting against a vertical wall. if the bottom of the ladder is being pushed…

A:

Q: The surface area of a sphere increases at a rate of 90 m/sec. Then the rate at which the radius…

A:

Q: A spherical balloon is being deflated at a rate of 80 cm³/min. At what rate is the radius decreasir…

A:

Q: A 60-kg skydiver jumps out of an airplane. What is her terminal velocity, in meters per second,…

A: Given, Mass (m) of the skydiver = 60-kg, and k = 10-kg/s

Q: A small rocket is launched straight up in the air at a speed of 4ft/sec. A camera on the ground, 10…

A: Consider the given information. At any time t, rocket is at C tanθ=ACAB=AC10

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: An inverted conical water tank with a height of 12ft and a radius of 6ft ft is drained through a…

A:

Q: As a circular metal griddle is being heated, its diameter changes at a rate of 0.01 cm/min. Find the…

A:

Q: The velocity function (in meters per second) is given for a particle moving along a line.

A:

Q: A car is slowing down at the rate 0.8 ft/sec². How far will the car move before it stops if its…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off…

A:

Q: An egg is thrown off the roof of a 60ft. building with an initial velocity of 6.5 ft/s. How long…

A: Given initial velocity = 6.5fts

Q: A 500-g ball at the level ground is kicked at a velocity of 30 m/s at an angle 25 degrees from…

A:

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

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: A rocket lifts off the surface of Earth with a constant acceleration of 20 m/sec2. How fast will the…

A:

Q: An object is thrown vertically upward from a point 32 feet above the ground with an initial velocity…

A:

Q: A person has a steel ball attached to a 6 foot long rope and is rotating the ball at the rate of 10…

A: Given, The length of the rope (r)is 6 foot =6 foot x 0.3048meter =1.8288 meters θ = number of…

Q: A vertical cylinder is leaking water at a rate of 8m^3/sec. if the cylinder has a height of 10m and…

A: In a vertical cylinder water is leaking at a rate of 8 m3/sec. dVdt=8 Height of the cylinder is 10…

Q: A Helium is being pumped into a spherical balloon at a rate of 12cm³/min. Determine the rate at…

A:

Q: An object is thrown vertically upward with an initial velocity of 16 ft/sec from the top of a house…

A:

Q: 3. Water is flowing out of a cylindrical storage tank at a rate of 2m/min. If the tank has a radius…

A:

Q: 5. A 6-ft man walks away from a 15-ft lamppost at a speed of 3 ft/s. Find the rate at which his…

A:

Q: A kite, 120 ft above the ground, is moving horizontally at the rate of 10 ft/sec. At what rate is…

A:

Q: A spherical balloon is being inflated at a rate of 9(pi)cm^3/sec. At what rate is its radius…

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: A conical cistern of height 5 ft and 7 ft across the top is being filled at a rate of 5 ft3/s while…

A: A conical cistern is given whose height is 5 ft and diameter at the top is 7 ft. A conical cistern…

Q: A ceiling fan has blades 61.0 cm long. What is the linear velocity of the tip of a blade when the…

A: Given the speed of the fan is : 8.50 revolutions per second⇒Angular velocity of the fan (ω)=8.50…

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: Air is being pumped into a spherical balloon at a rate of 4 cm3/min. Determine the rate at which the…

A:

Q: A ball is shot straight up into the air with initial velocity of 49 ft/sec. Assuming that the air…

A: See the details solution in below

Q: . A kite 100 ft above the ground moves horizontally at aspeed of 8 fts. At what rate is the angle…

A: At what rate is the angle between the stringand the horizontal decreasing when 200 ft of string has…

Q: 1. A particle moving along in a straight line with a uniform acceleration covers 72 cm displacement…

A: