A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is e. The distance (in meters) the ball bearing rolls in t seconds is s(t) = 4.9(sin 0)t2.(a) Determine the speed of the ball bearing after t seconds.m/s(b) Complete the table.n/4A/37/2s'(t)2x/3Зл/4s'(t)Use the table to determine the value of 0 that produces the maximum speed at a particular time.

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Answered: A ball bearing is placed on an inclined…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is given by a(t)=-sin(t). At the time t = 0, its position is x = 3. (a) Find the velocity and position functions for the particle. (b) Find the values of t for which the particle is at rest.
Suppose a projectile is fired at an angle of elevation θ with an initial velocity of v0 ft/sec. In calculus and physics courses you will learn that points (x(t), y(t)) on the path of the projectile at time t are given by x(t) = (v0 cos θ)t, y(t) = (v0 sin θ)t −1/2 gt^2 where g = 32 f t/sec2 is the acceleration due to the earth’s gravity. Where will a projectile land if it is fired at an angle of 30 degrees and an initial velocity of 400 ft/sec?
a quarterback throws a football with an initial velocity of 72 ft/sec at an angle of 25. the height of a ball can be modeled by h(t) = -6t^2 + 30.4t +5 where h(t) is the height (in ft) and t is the time seconds after release. a, Determine the time at which the ball will be at its maximum height. b, Determine the maximum height of the ball. c, Determine the amount of time required for the ball to reach the reciver's hands if the receiver catches the ball at a point 3 ft off the ground.
8. A dock is 6 feet above water. Suppose you stand on the edge of the dock and pull a rope attached to a boat at the constant rate of 2 ft/s. Assume that the boat remains at water level. At what speed is the boat approaching the dock when it is 20 feet from the dock? 10 feet from the dock? Isn't it surprising that the boat's speed is not constant? 9. Evaluate sin x dx a) Jisinx b) (secx tan x- cse²x d secx + cot x 10. Use Riemann sums and a limit to compute the exact area under the curve y = f(x) = 2x² + 1 on the interval [1,3].
Finf the equation of the tangent line to (cos(x)ex10x)/(Sec2(5x)+1)+11 at the point (0,11)
The temperature in degrees Celsius on the surface of a metal plate is given by T(x, y), where x and y are measured in centimeters. Find the direction from point P where the temperature increases most rapidly and this rate of increase. T(x, y) = 80 − 3x2 − y2, P(−1, 5)
A particle moves along a line with velocity function v(t) =t2 -t, where is measured in meters per second.Find (a) the displacement and (b) the distance traveled bythe particle during the time interval [0,5].
A spherical dust particle, with a radius a=0.11mm and density of 1030kg/m3, is sedimenting in the quiescent air that has a viscosity of μ=1.81×10−5 kg/m⋅s. The particle experiences the gravitational force, with g=9.81m/s2, as well as a friction force from the viscous air that can be described by F=−6πμaU, where U is the instantaneous velocity of the particle. The motion of the particle is governed by the Newton's second law. At the time t=0, the dust particle has a downward speed of 0.17m/s. Use the Euler's method, and a time step of h=0.1s, calculate: When t=0.1s, the downward speed of the dust particle is m/s
A sky diver weighing 192 lb (including equipment) falls vertically downward from a very high altitude. Assume that the air resistance is proportional to the falling velocity with the constant k = 0.6, the acceleration due to gravity g = 32ft/sec2, and that the positive direction is downward. What is the terminal velocity of the sky diver if he/she never opens the parachute?

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