A ping-pong ball is moving along a track so that its position at time t is give by the vector , where x(t) = 212-6t+3 and y(t) is unknown. Both x and y are measured in meters, and t is measured in seconds. It is know that the velocity of the ping-pong ball in the dy =te-2-3. dt y-direction is given by
A ping-pong ball is moving along a track so that its position at time t is give by the vector , where x(t) = 212-6t+3 and y(t) is unknown. Both x and y are measured in meters, and t is measured in seconds. It is know that the velocity of the ping-pong ball in the dy =te-2-3. dt y-direction is given by
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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Please solve part D -- all three parts to Part D. Please help with this, and no AI Please. I need to understand this. Thank you
Transcribed Image Text:A ping-pong ball is moving along a track so that its position at time t is give by the vector
<x(t), y(t)>, where x(t) = 2t2-6t+3 and y(t) is unknown. Both x and y are measured in
meters, and t is measured in seconds. It is know that the velocity of the ping-pong ball in the
y-direction is given by
dy
dt
=te-2-3.
(a) Find the time t, 0 <t≤3, when the line tangent to the path of the particle is vertical. Is
the ping-pong ball flying up or down right at that time? Give a reason for your answer
(b) Find the speed of the ping-pong ball at t=2 seconds.
(c) Find the total distance traveled by the ping-pong ball during the first 3 seconds 0≤t≤3.
(d) There are two points along the track 3 meters to the right of the origin through which the
ping-pong ball passes.
(i) Find the two values of t when that occurs.
(ii) Find the slope of the lines tangent to the ball's path at that point.
(iii) Find the y-coordinate of these points given y(1) = 6.
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VIEWStep 2: d(i) Determining the two values of t when the two points along the track 3 meters to the right
VIEWStep 3: d(ii) Determining the slope of the lines tangent to the ball's path at that point
VIEWStep 4: d(iii) Determining the y-coordinates of these points
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