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5. A ball is thrown upward in the air with a velocity of 12 m/s and its height after t seconds is given by h=12t-4.91². Use Calculus methods to determine the following: a. Find the velocity when t = 2 s. b. When will the ball hit the ground? c. With what velocity will the ball hit the ground?

5. A ball is thrown upward in the air with a velocity of 12 m/s and its height after t seconds is given by h=12t-4.91². Use Calculus methods to determine the following: a. Find the velocity when t = 2 s. b. When will the ball hit the ground? c. With what velocity will the ball hit the ground?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve problem 5 please. Thanks
3. Explain why the given function is discontinuous at x = 1: ƒ(x) = { x² − 1, x = 1 4. Find the equation of the tangent and the normal lines to the curve y=- y=4 at the point (4,1). 5. A ball is thrown upward in the air with a velocity of 12 m/s and its height after t seconds is given by h=12t-4.91². Use Calculus methods to determine the following: a. Find the velocity when t = 2 s. b. When will the ball hit the ground? c. With what velocity will the ball hit the ground? 6. If the tangent line to y = f(x) at (2, 4) passes through the point (5,10), find ƒ(2) and f'(2). 7. Differentiate: a. f(t)=- b. f(x) = 57⁹ c. y =(√x+1)·(e*) d. f(x) = e* sin 2x - x³ cos 3x 79-t 4+t te' 8. Find the second derivative of f(x) = ln(xe¯5x).
Transcribed Image Text:3. Explain why the given function is discontinuous at x = 1: ƒ(x) = { x² − 1, x = 1 4. Find the equation of the tangent and the normal lines to the curve y=- y=4 at the point (4,1). 5. A ball is thrown upward in the air with a velocity of 12 m/s and its height after t seconds is given by h=12t-4.91². Use Calculus methods to determine the following: a. Find the velocity when t = 2 s. b. When will the ball hit the ground? c. With what velocity will the ball hit the ground? 6. If the tangent line to y = f(x) at (2, 4) passes through the point (5,10), find ƒ(2) and f'(2). 7. Differentiate: a. f(t)=- b. f(x) = 57⁹ c. y =(√x+1)·(e*) d. f(x) = e* sin 2x - x³ cos 3x 79-t 4+t te' 8. Find the second derivative of f(x) = ln(xe¯5x).
Expert Solution
Step 1

a.

Consider the given function,

h=12t-4.9t2                             …1

where h is height and t is time.

It is required to find the velocity of ball at t=2 s.

Now, differentiate with respect to time the given function to find the at any time t,

dhdt=ddt12t-4.9t2V=12-9.8t                           …2

Now, put t=2,

V=12-9.82=12-19.6=-7.6

Hence, the velocity of the ball is -7.6 ms and the negative sign shows that ball is moving downward.

 

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