Explanation Given Information: The height of the Washington Monument from ground level to the top is 555 feet . Formula used: The constant rule of integration , ∫ k d x = k x + C . The simple power rule of integration, ∫ x n d x = x n n + 1 + C . The zero property of multiplication, if a ⋅ b = 0 the either a = 0 or b = 0 . Calculation: Consider the height of the object thrown upward is s . The acceleration function due to gravity in downward direction is 32 feet p e r s e c o n d p e r s e c o n d . s ' ' ( t ) = − 32 Integrate both sides, use the constant rule of integration ∫ k d x = k x + C . ∫ s ' ' ( t ) d t = − ∫ 32 d t s ' ( t ) = − 32 t + C 1 Here, s ' ( t ) is the velocity of the object at time t . Consider the initial velocity of the object is v 0 . Substitute 0 for t in the velocity function s ' ( t ) = − 32 t + C 1 for initial velocity condition. s ' ( 0 ) = − 32 ( 0 ) + C 1 = C 1 The initial velocity of the ball thrown upward is given as, s ' ( 0 ) = v 0 Substitute v 0 for s ' ( 0 ) in above function for initial velocity condition. v 0 = 0 + C 1 C 1 = v 0 Substitute v 0 for C 1 in velocity function s ' ( t ) = − 32 t + C 1 s ' ( t ) = − 32 t + v 0 Integrate both side the above velocity function, use the simple power rule of integration ∫ x n d x = x n n + 1 + C ∫ s ' ( t ) d t = − ∫ ( 32 t + v 0 ) d t s ( t ) = − 32 ( t 1 + 1 1 + 1 ) + v 0 t + C 2 = − 32 ( t 2 2 ) + v 0 t + C 2 = − 16 t 2 + v 0 t + C 2 Substitute 0 for t in above height function for initial condition

10th Edition

ISBN: 9780357265161

Author: Larson

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 5.1, Problem 67E

To determine

To calculate: The initial velocity requires to throw an object upward (from ground level) to the top of the Washington Monument (555 feet).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.1, Problem 66E

Chapter 5.1, Problem 68E

Students have asked these similar questions

You are on an airplane. The pilot announces the plane’s speed over the intercom. Which speed do you think is being reported: the speed of the plane in still air or the speed after the effect of the wind has been accounted for? Explain your answer.

How would u answer this?

A Ferris wheel at a theme park rotates in an anticlockwise direction at a constant rate. People enter the cars of the Ferris wheel from a platform which is above ground level. The Ferris wheel does not stop at any time. The Ferris wheel has 16 cars, spaced evenly around the circular structure. A spider attached itself to the point P on the side of car C when the point P was at its lowest point at time 1.00 pm. The height, h metres, of the point P above ground level, at time t hours after 1.00 pm is given by h(t)=62+60 sin(((5t-1)pi)/2) a) Write down the maximum height, in metres, of the point P above ground level. b)Write down the minimum height, in metres, of the point P above ground level. c) At what time, after 1.00 pm, does point P first return to its lowest point? d)Find the time, after 1.00 pm, when P first reaches a height of 92 metres above ground level. e)Find the number of minutes during one rotation that P is at least 92 metres above ground level.

Chapter 5 Solutions

CALCULUS: APPLIED APPROACH LOW COST MA

Ch. 5.1 - Checkpoint 1 Worked-out solution available at...Ch. 5.1 - Prob. 2CP Ch. 5.1 - Prob. 3CP Ch. 5.1 - Prob. 4CP Ch. 5.1 - Prob. 5CP Ch. 5.1 - Prob. 6CP Ch. 5.1 - Checkpoint 7 Worked-out solution available at...Ch. 5.1 - Prob. 8CP Ch. 5.1 - Prob. 1SWU Ch. 5.1 - Prob. 2SWU

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The initial velocity requires to throw an object upward (from ground level) to the top of the Washington Monument ( 555 feet ) .

Solution Summary: The author calculates the initial velocity required to throw an object upward (from ground level) to the top of the Washington Monument.

Concept explainers

Videos

To calculate: The initial velocity requires to throw an object upward (from ground level) to the top of the Washington Monument (555 feet).

Want to see the full answer?

Chapter 5 Solutions