At what points on the given curve x = smaller x-value (x, y) = larger x-value (x, y) = 2t3, y=3+ 40+ 11+² does the tangent line have slope 1? A major league baseball pitcher throws a pitch that follows these parametric equations: x(t) = 146t y(t)=-16t² + 6 + 5. The time units are seconds and the distance units are feet. The distance between the location of the pitcher and homeplate (where the batter stands) is 60.5 feet. Give EXACT answers, unless instructed otherwise. (a) Calculate the horizontal velocity of the baseball at time t; this is the function x'(t)= | 146 (b) What is the horizontal velocity of the baseball when it passes over homeplate? 146 (c) What is the vertical velocity of the baseball at time t; this is the function y'(t)=-32t+6 (d) Recall that the speed of the baseball at time t is s(t)=√ [x '(t)]² + [y' (t)]² ft/sec. What is the speed of the baseball (in mph) when it passes over homeplate? (e) At what time does the baseball hit the ground, assuming the batter and catcher miss the ball? (f) What is the magnitude of the angle at which the baseball hits the ground? mph. ft/sec ft/sec. ft/sec. sec. rad. (This is the absolute value of the angle between the tangential line to the path of the ball and the ground. Give your answer in radians to three decimal places.)
At what points on the given curve x = smaller x-value (x, y) = larger x-value (x, y) = 2t3, y=3+ 40+ 11+² does the tangent line have slope 1? A major league baseball pitcher throws a pitch that follows these parametric equations: x(t) = 146t y(t)=-16t² + 6 + 5. The time units are seconds and the distance units are feet. The distance between the location of the pitcher and homeplate (where the batter stands) is 60.5 feet. Give EXACT answers, unless instructed otherwise. (a) Calculate the horizontal velocity of the baseball at time t; this is the function x'(t)= | 146 (b) What is the horizontal velocity of the baseball when it passes over homeplate? 146 (c) What is the vertical velocity of the baseball at time t; this is the function y'(t)=-32t+6 (d) Recall that the speed of the baseball at time t is s(t)=√ [x '(t)]² + [y' (t)]² ft/sec. What is the speed of the baseball (in mph) when it passes over homeplate? (e) At what time does the baseball hit the ground, assuming the batter and catcher miss the ball? (f) What is the magnitude of the angle at which the baseball hits the ground? mph. ft/sec ft/sec. ft/sec. sec. rad. (This is the absolute value of the angle between the tangential line to the path of the ball and the ground. Give your answer in radians to three decimal places.)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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Transcribed Image Text:At what points on the given curve x =
smaller x-value
(x, y) =
larger x-value
(x, y)
=
2t3, y=3+ 40+ 11+² does the tangent line have slope 1?
![A major league baseball pitcher throws a pitch that follows these parametric equations:
x(t) = 146t
y(t)=-16t² + 6 + 5.
The time units are seconds and the distance units are feet. The distance between the location of the pitcher and homeplate (where the batter stands) is 60.5 feet. Give EXACT answers, unless instructed otherwise.
(a) Calculate the horizontal velocity of the baseball at time t; this is the function x'(t)= | 146
(b) What is the horizontal velocity of the baseball when it passes over homeplate? 146
(c) What is the vertical velocity of the baseball at time t; this is the function y'(t)=-32t+6
(d) Recall that the speed of the baseball at time t is
s(t)=√ [x '(t)]² + [y' (t)]² ft/sec.
What is the speed of the baseball (in mph) when it passes over homeplate?
(e) At what time does the baseball hit the ground, assuming the batter and catcher miss the ball?
(f) What is the magnitude of the angle at which the baseball hits the ground?
mph.
ft/sec
ft/sec.
ft/sec.
sec.
rad. (This is the absolute value of the angle between the tangential line to the path of the ball and the ground. Give your answer in radians to three decimal places.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5e3918c-0667-402f-8416-7840e886e6c8%2F0a653f80-b422-4d71-9840-18bc8a8935d3%2Fjb7wgvd_processed.png&w=3840&q=75)
Transcribed Image Text:A major league baseball pitcher throws a pitch that follows these parametric equations:
x(t) = 146t
y(t)=-16t² + 6 + 5.
The time units are seconds and the distance units are feet. The distance between the location of the pitcher and homeplate (where the batter stands) is 60.5 feet. Give EXACT answers, unless instructed otherwise.
(a) Calculate the horizontal velocity of the baseball at time t; this is the function x'(t)= | 146
(b) What is the horizontal velocity of the baseball when it passes over homeplate? 146
(c) What is the vertical velocity of the baseball at time t; this is the function y'(t)=-32t+6
(d) Recall that the speed of the baseball at time t is
s(t)=√ [x '(t)]² + [y' (t)]² ft/sec.
What is the speed of the baseball (in mph) when it passes over homeplate?
(e) At what time does the baseball hit the ground, assuming the batter and catcher miss the ball?
(f) What is the magnitude of the angle at which the baseball hits the ground?
mph.
ft/sec
ft/sec.
ft/sec.
sec.
rad. (This is the absolute value of the angle between the tangential line to the path of the ball and the ground. Give your answer in radians to three decimal places.)
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