The equation for free fall at the surface of some planet (s in meters, t in seconds) is s = 5.88t2. How long does it take a rock falling from rest to reach a velocity of 23.3 m/s on this planet? ..... It takes sec for a rock falling from rest to reach a velocity of 23.3 m/s. (Round to the nearest tenth as needed.)

Q: You start riding your bike east at 16mph. At the same time and from the same spot, your friend…

A: Given that You start riding your bike east at 16mph. At the same time and from the same spot, your…

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: If an arrow is shot upward on the moon with a velocity of 58 ms, its height (in meters) after t…

A: When the arrow hits the moon then the height is 0. So, H=0 We will find t for H=0

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: If a rock is thrown upward on the planet Mars with a velocity of 10m/s, its height (in meters) after…

A: This is application of derivative problem

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: A particle moves along a straight line with a velocity v(t) =t*e meters per second after t seconds.…

A:

Q: The acceleration of a Maserati is proportional to the difference between 250 km/h and the velocity…

A:

Q: A box weighing 50lbs falls from rest and the air resistance is proportional to his speed V and that…

A: We need to find velocity.

Q: If the brakes on a car give the car a constant negative acceleration of 2k m/s?, where k is a…

A: The given question has been solved in detail.

Q: A projectile is launched from ground level with an initial velocity of v0 feet per second.…

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Q: The position from its starting point of a small plane preparing for takeoff is given by x(1) = 1.412…

A:

Q: Find the distance traveled after 6 seconds by a particle whose velocity is v(t) = (t − 2) meters at…

A: Given

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: An arrow is shot vertically upward from a platform 25 ft high at a rate of 172 ft/sec. When will the…

A:

Q: The mass of a cube in grams is M=x^3+0.1x^4, where is the length of one side in centimeters. If the…

A:

Q: If a ball is thrown directly upward with a velocity of 42 ft/s, its height (in feet) aftert seconds…

A:

Q: The rate at which bacteria multiply is proportional to the instantaneous N numbers present. If the…

A: Let y(t) represents the number of bacteria present in the culture after t hours. Let the initial…

Q: Suppose that the acceleration of a vehicle at time t (in s) is given by a(t) = 2t+ 1 (mph/s).If the…

A:

Q: Two cars start moving from the same point. One travels south at 32 mi/h and the other travels west…

A:

Q: A man cruises his new model Ferrari north 8 mi and then turns east at 12 mi/hr. At what rate was his…

A: Explained below

Q: At noon, ship A is sailing north at a speed of 7mph, at the same time ship B, 5 miles west of ship…

A: Given, at noon, Ship A is sailing north at a speed of 7mph. At the same time, Ship B, which is 5…

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

A: Consider the given:

Q: If a ball is thrown directly upward with a velocity of 46 ft/s, its height (in feet) after t seconds…

A:

Q: An airplane at an altitude of 35,000 feet begins descending at a rate of 2,000 feet per minute. How…

A:

Q: The rate at which the body cools is proportional to the difference in temperature of the body and…

A:

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

A:

Q: How far above the surface of the Earth would he have to go to "lose" 13 % of his body weight?…

A: Follow the procedure given below.

Q: At what fraction of the speed of light does Alice have to travel relative to Bob so that Alice does…

A: Given Alice does everything three times as slowly as Bob Find The fraction of speed

Q: A 45-caliber bullet shot straight up from thesurface of the moon would reach a height of s = 832t -…

A: Given, A 45-caliber bullet shot straight up from the surface of the moon would reach a height of…

Q: At what rate is the distance between Jack and Jill changing if Jack is 3 miles from the bakery and…

A: Given:         To determine:

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

A:

Q: A 2.63-kg steel ball is dropped from a plane to an ocean. If the velocity of the ball just before…

A:

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

A:

Q: A steel ball of mass 4 kg is dropped from a building. If the air resistance is equal to 0.371v, what…

A: Mass of ball m=4 kg Air Resistance =0.371v Now, the formula to find  velocity of ball at time t is:…

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

A:

Q: a 5-ft tall person walks away from a 20-ft tall streetlamp at a constant rate of 3 ft/s . at which…

A: Let us denote: x= distance of the person from the post y=length of the shadow Given that, dx/dt=3 ,…

Q: If a ball is thrown directly upward with a velocity of 46 ft/s, its height (in feet) after t seconds…

A: Given function  y = 46t − 16t2y = -16t2+46t+0 This is function of inverted parabola. Its maximum…

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 directly upward with a velocity of 44 ft/s, its height (in feet) after t seconds…

A: For Maximisation put the roots of f’(x) to the double derivative function, f’’(x) to see if it is…

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

A:

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: 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: light is 25 ft above a sidewalk and a man 6 ft tall is walking away from the point under the light.…

A:

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

A:

Q: The deck of a bridge is suspended 295 feet above a river. If a pebble falls off the side of the…

A: The deck of a bridge is suspended 295 feet above a river. If a pebble falls off the side of the…

Q: A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32…

A: