A rocket can rise to a height of h(t) = + 0.6t2 feet in t seconds. Find its velocity and acceleration 14 seconds after it is launched. velocity ft/s acceleration ft/s?

Q: hot air ballon is hovering 110 meters above the ground and begins to assend at a rate of 17 meters…

A: This is a question of application of differentiation and integration... We will proceed as follows

Q: A5 feet 6 inches tall man is walking away from a lamppost at a rate of 2 ft/sec. If the lamppost is…

A: We have, A 5 feet 6 inches (5.5 feet) tall man is walking away from the lamppost of height 12 feet…

Q: A car is traveling at 100 km/h when the driver sees an accident 80 m ahead and slams on the brakes.…

A: Given data:   The initial speed of the car is u=100 km/h. The given distance is s=80 m=0.08 km.…

Q: A cyclist coasts up a 11.3° slope, traveling 19.0 m along the road to the top of the hill. If the…

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Q: Suppose you drive for 60 miles at 60 miles per hour, then for 60 miles at 30miles per hour. In miles…

A: Recall the equation connecting the three variables of speed, distance and time as: time = distance /…

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

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Q: Find the rate at which the water level is rising when the water level is 2 cm.

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Q: Each side of a square is increasing at a rate of 6 cm/s . Atwhat rate is the area of the square…

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Q: A golfer takes a swing from a hill twenty feet above the cup with an initial upwards velocity of 32…

A: It is given that, initial upward velocity from the hill is, v=32 feet per second, angle of swing…

Q: A candle on Pauline dresser is 4 inches tall.and burns at a rate of 0.6 inches per hour . How many…

A: Topic - equation in one variable

Q: One speed skater starts across a frozen lake at an average speed of 9 m/s. Ten seconds later, a…

A: Let t= time in second d=distance Also, consider second skater time in second is t .

Q: A 6-foot-tall woman walks at 7 ft/s toward a street light that is 30 ft above the ground. What is…

A: Let L be the length of the woman's shadow  x be woman's distance from the street light dLdt=rate of…

Q: Water flows from the bottom of a storage tank at a rate of r(t)=350– 5t litres per minute, where…

A: Given that the water flow from the bottom of a storage tank at a rate, rt=350-5t,  0≤t≤80

Q: After 2 days, 10 grams of a radioactive substance is present. Three days later, 5 grams is present.…

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Q: An object is dropped from a 64-foot tower and reaches the ground in 2 seconds. What would the…

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Q: Suppose a car is going 31 miles per hour and slams on the break and decelerates at 13 feet per…

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Q: A 200-liter tank initially full of water develops a leak at the bottom. Given that 10% of the water…

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Q: The velocity v of a falling object is directly proportional to the time t of the fall. If, after 2…

A: What will its velocity be after 3 seconds?

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

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Q: A cannonball is fired directly upward from a height of 0 feet, with an initial velocity of 220 feet…

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Q: On the moon, the acceleration of a free-falling object is a(t) = −1.6 meters per second per second.…

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Q: Romeo is walking towards North at a rate of 4m/s. Ten seconds after, Juliet walks towards East at a…

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Q: A population of bacteria is growing according to the equation P(t) 1250e".11. Estimate when the…

A: The population of bacteria growing according to the equation We need to find the value of t when…

Q: Assume the learning rate for new skills is proportional to the difference between the maximum…

A: The learning rate for new skills is proportional to the difference between the maximum potential for…

Q: After 2 days, 10g of radioactive chemical is present. Three days later, 5g is present. How much of…

A: Given:      After  2 days, 10g of radioactive chemical is present. Three days later5 g chemical is…

Q: snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate (in cm/min)…

A: Given query is to find the rate at which diameter of snowball is decreasing.

Q: A projectile is shot upwards from the surface of the earth with an initial velocity of 120 meters…

A: To determine: The velocity of a projectile after 6 seconds and after 9 seconds where a projectile is…

Q: On the moon, the acceleration due to gravity is 1.6 m/sec2. If a rock is dropped into a crevasse,…

A: Consider the given value of acceleration due to gravity 1.6 m/sec2.

Q: Jessi launched a toy rocket vertically upward having an initial velocity of 100 feet per second then…

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Q: A particle moving along a straight line has a velocity of v(t) = t² e-t feet per second after t sec.…

A: Given: A particle moving along a straight line has a velocity of v(t)=t2e-t feet per second after t…

Q: A rocket rising from the ground has a velocity of v(t)=2,000 te-t/180 ft/s, after t seconds. How far…

A: Given thatThe velocity of the rocket rising from the ground is

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

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Q: A dynamite blast blows a heavy rock straight up with a launch velocityof 160 ft/sec (about 109 mph)…

A: Rock reaches a height of

Q: A car traveling at 60 mi/h (88 ft/s) skids 176 ft after its brakes are suddenly applied. Under the…

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Q: On Earth, you can easily shoot a paperclip 64 ft straight up into the air with a rubber band. In t…

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Q: What is the velocity (in ft/s) of a sandbag 3.0 s after it is released from a hot-air balloon that…

A: According to Questions  Initial velocity (u)=0 ft/s  time=t=3s

Q: on the moon, the acceleration of a free falling object is a(t) = -1.6 meters per second per second.…

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Q: A car is traveling at  100km/h when the driver sees an accident80 m ahead and slams on the brakes.…

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Q: After a ball bounces off from the top of a hill, its velocity at t seconds is v(t)=45-30t feet per…

A: Given velocityv(t) = 45 - 30t

Q: If a ball is thrown into the air with a velocity of 42 ft/s, its height (in feet) after t seconds is…

A: Given, The height of the ball is given by : y = 42t -16t2 ;  Where y is in feet and t is in seconds…

Q: A car drives with velocity v(t)=2.8+/t meters per second. How far does the car drive in 8 seconds?…

A: Given data: The velocity of car is vt=2.8+t. Time taken by car is t = 8 s.

Q: On Earth, you can easily shoot a paper clip 64 ft straight up into the air with a rubber band. In t…

A: #a) We find the velocity of the clip using first derivative.

Q: After an hour, the population of bacteria with a number of P0 found that their number became 3 /…

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Q: What is the velocity of flow in feet per seconds f

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

Q: ng the shore and 60 meters from the sh mps into the water and swims from the second and swim at a…

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Q: A baseball thrown directly upward at 160 ft/sec has velocity v(t) = 160- 32t ft/sec at time t…

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Q: escape velocity

A: We shall assume an initial velocity in a radial direction so that the motion of the particle takes…