what speed must you toss a ball straight up so that it takes 4 s to return to you?

Excursions in Physics

Homework, Affiliate 3: Linear Move

Ch 3, Linear Movement; Ex 22, 24, 27, 34, 37; Pb 2, three, iv, 6

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Exercises (Discussion Questions)

Ex iii.22 Suppose that a freely falling object were somehow equipped with a speedometer. By how much would its speed reading increment with each second of autumn?

Every second, its speed increases past 10 m/s. That means its acceleration is 10 (yard/s)/s.

Ex 3.24 For a freely falling object dropped from rest, what is its acceleration at the end of the 5th 2nd of fall? The 10th second? Defend your reply.

The acceleration of a freely falling object is abiding so its acceleration at the terminate of the 5th second is the same every bit its acceleration at the terminate of the tenth second--or the finish of the first 2d or the start of the 17th second. Its acceleration is 9.eight one thousand/s/s -- which we will gauge equally well-nigh 10 g/s/s.

Ex iii.27 Someone standing at the edge of a cliff (every bit in Effigy three.8) throws a ball straight upwards at a certain speed and another ball directly down with the same initial speed. If air resistance is negligible, which ball will take the greater speed when information technology strikes the ground beneath? Explain.

First, consider the ball thrown up. Information technology continues to move up equally information technology slows and then comes to a stop at the top of its path and and so starts to increase its speed downward. When it gets dorsum to its original position at the border of the cliff, it has the same speed as information technology did initially when information technology was thrown up; it is moving in the reverse direction (downward, this fourth dimension) just has the same speed. It will continue on and hit the footing below. Its move from the cliff on down to the ground, and then, will be exactly the same equally the move of a ball thrown down with this aforementioned speed.

That means the two balls striking the basis with the same speed.

Ex 3.34 Extend Tables 3.2 and 3.3 (which give values of time from 0 to five s) to 0 to 10 due south, assuming no air resistance.

time	velocity	distance fallen
( seconds)	( g/s )	( meters )
0	0	0
1	x	5
2	20	twenty
three	thirty	45
4	40	eighty
five	fifty	125
6	sixty	180
vii	70	245
8	80	320
nine	90	405
10	100	500
t	(ten) t	(1/2) (x) t2

Ex 3.37 In this affiliate, we studied idealized cases of balls rolling downward smooth planes and objects falling with no air resistance. If a classmate complains that all this attending focused on idealized cases is valueless because arcadian cases but don't occur in the everyday world, how would yous respond? How exercise you lot suppose the author of this volume or the instructor of this course would reply?

The motion of arcadian systems is far easier to understand. Once that motion is understood--as a starting time approximation--the move with friction (such as air resistance) is so easier to understand as a refinement to the get-go approximation.

(Numerical) Issues

Atomic number 82 iii.2 What is the acceleration of a vehicle that changes its velocity from 100 km/h to a expressionless cease in x s

The change in velocity is 5 = v_f - v_i = 0 - 100 km/h = - 100 km/h. The minus sign is important; don't forget to include it. The acceleration is a = v / t = ( - 100 km / h ) / 10 south = - x (km/h) / south or a = - 10 km/h/s.

Pb 3.three A brawl is thrown straight up with an initial speed of thirty yard/s. How high does information technology go, and how long is it in the air (neglecting air resistance)?

It is easier to begin by asking "how long is information technology in the air?" On the style up, its speed decreases by 10 m/s. At the end of the commencement second it is moving up at 20 m/s. At the end of the 2d second, it is moving upwardly at 10 m/s. At the cease of the third second, its speed (and velocity) is (or are) null; it stops for simply an instant. So information technology takes 3 seconds to go upwardly to its highest position. The motion is symmetric. Information technology will have and additional three seconds to fall dorsum downwards to its original position.

And then it is in the air for a total of six seconds.

Now we can ask "how high does it go?" It may be easier to think of this as "how far does it fall in three seconds?" It falls from residual and we have adult the equation southward = ¹/₂ a t² or y = ⁱ/_two a tⁱⁱ so we tin can utilize that

y = ⁱ/₂ a t²

y = ^ane/₂ (x m/s²) ( 3 s )²

y = 45 g

Pb 3.4 A ball is thrown with enough speed straight up and so that information technology is in the air several seconds.

(a) What is the velocity of the ball when it gets to its highest point?

At the top, its velocity is zero.

(b) What is its velocity 1 south earlier it reaches its highest bespeak?

One second before reaching the top, it is moving up at v = ten m/s.

(c) What is the alter in its velocity during this 1-south interval?

5 = v_f - v_i = 0 - ten m/south = - 10 1000/due south

(d) What is its velocity 1 s after it reaches its highest point?

One 2d after reaching the meridian, information technology is moving downwardly a v = - 10 k/s; the minus sign on the velocity indicates that information technology is, indeed, moving downwardly.

(due east) What is the change in velocity during this 1-s interval?

v = 5_f - v_i = 10 k/s - 0 = - 10 m/s

(f) What is the alter in velocity during the two-s interval?

5 = v_f - five_i = - x m/south - x yard/due south = - xx k/s

(k) What is the acceleration of the ball during any of these time intervals and when it passes through the aught velocity point?

a = v / t

For part (c), this is a = 5 / t = ( - 10 yard/s) / (1 s) = - 10 thousand/sⁱⁱ.

For function (east), this is a = v / t = ( - 10 grand/due south) / (i due south) = - 10 m/southward².

For office (d), this is a = 5 / t = ( - 20 m/s) / (ii s) = - 10 m/s².

This illustrates that the acceleration is abiding; the acceleration is ever a = - 10 m/s². That is true on the style upward, on the style down, and even at the moment the brawl is at the very top of its path.

Pb 3.6 A car takes x s to go from v = 0 to v = xxx m/s at approximately abiding acceleration. If you wish to find the distance traveled using the quation d = (^ane/₂) a t^{2, what value should you apply for a?}

Acceleration a is the change in velocity divided by the change in time,

a = v / t

v = 5_terminal - 5_initial

5 =30 ^m/_s - 0 = thirty ^{one thousand/_s}

t = 10 due south

a = five / t = [30 ^yard/_s ] / 10 south

a = 3 m/s/southward

a = 3 1000/southward²

Let'south go ahead and really calculate how far the car travels during that x fourth dimension;

d = (¹/₂) a tⁱⁱ

d = (0.5)(3 1000/s²)(x s)^two

d = (0.v)(3 grand/s²)(100 s^two)

d = 150 g

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Typical or possible multiple-choice questions over this material:

1. Kinematics is a description of move. Motility was outset well understood

a) by Aristotle and the aboriginal Greeks

b) by Ptolemy in Egypt

c) by Galileo in Italy

d) not until the commencement of the twentieth century

2. To measure the time needed to investigate move,

a) Aristotle used the pendulum clock which had only been invented

b) Ptolemy used a sundial

c) Galileo invented his ain water clocks

d) Newton invented the pendulum clock

3. What is the average speed of a motorcycle that travels twenty chiliad in 2 s?

a) 40 g/south

b) 20 m/southward

c) 10 yard/s

d) ix.8 m/s

4. What is the average speed of a car that travels 45 km in iii h?

a) 135 km/h

b) 15 km/h

c) 10 km/h

d) 9.viii km/h

five. Consider a railroad train that has an dispatch of 3 m/s². Initially, at time t = 0, information technology has a velocity of v_i = 10 chiliad/southward. What is its speed at t = 3 southward?

a) twoscore m/s

b) thirty yard/southward

c) 23 m/due south

d) 19 grand/southward

6. Consider a car that starts at rest and accelerates at two thousand/due south² for iii seconds. At that time, t = iii s, how fast is it going?

a) 12 m/s

b) ix thou/due south

c) 6 m/s

d) 3 one thousand/s

7. Consider a car that starts at rest and accelerates at two thou/southwardⁱⁱ for 3 seconds. At that time, t = 3 s, how far has information technology gone?

a) 12 yard

b) 9 1000

c) half dozen thou

d) 3 k

viii. Consider a ball that is thrown upward at the edge of a canyon with an initial velocity of 20 grand/due south. Three seconds later, what is its velocity?

a) xxx yard/southward

b) 15 chiliad/s

c) - 10 m/s

d) - 30 k/s

9. Consider a ball that is thrown direct upward at the border of a canyon with an initial velocity of 20 m/s. 3 seconds later, where is it located? Take its initial position, at the edge of the canyon, to be the origin; that is, y_i = 0.

a) 30 one thousand

b) 15 thousand

c) - ten one thousand

d) - 30 thou

Answers to the multiple-guess questions:

i. Kinematics is a description of motion. Motion was first well understood

a) by Aristotle and the ancient Greeks

b) by Ptolemy in Arab republic of egypt

c) by Galileo in Italia

d) not until the commencement of the twentieth century

two. To measure the time needed to investigate motion,

a) Aristotle used the pendulum clock which had simply been invented

b) Ptolemy used a sundial

c) Galileo invented his own water clocks

d) Newton invented the pendulum clock

3. What is the boilerplate speed of a motorbike that travels twenty m in 2 s?

a) 40 m/s

b) 20 m/s

c) 10 yard/s; v = xx thou / 2 southward = 10 m/due south

d) 9.8 m/s

four. What is the average speed of a machine that travels 45 km in 3 h?

a) 135 km/h

b) xv km/h; five = 45 km / 3 h = 15 km/h

c) x km/h

d) 9.8 km/h

5. Consider a train that has an acceleration of 3 grand/southward². Initially, at time t = 0, it has a velocity of v_i = x m/s. What is its speed at t = 3 south?

a) 40 k/s

b) 30 chiliad/s

c) 23 g/s

d) 19 g/south; five = 5_i + a t = 10 m/s + (3 m/southwardⁱⁱ) (3 southward) = (ten + nine) m/s = 19 g/due south

6. Consider a car that starts at balance and accelerates at 2 m/southward² for iii seconds. At that time, t = 3 s, how fast is it going?

a) 12 g/south

b) ix m/s

c) 6 m/s; v = v_i + a t = 0 + (2 thou/sⁱⁱ) (3 s) = six m/south

d) 3 chiliad/s

7. Consider a automobile that starts at balance and accelerates at 2 chiliad/s² for 3 seconds. At that time, t = 3 due south, how far has it gone?

a) 12 m

b) nine k; x = x_i + v_i t + (¹/₂) a t² = 0 + 0 + (ⁱ/₂) (2 m/due southⁱⁱ) (3 s)² = 9 m

c) vi m

d) 3 m

viii. Consider a ball that is thrown upward at the edge of a canyon with an initial velocity of 20 grand/s. Three seconds later, what is its velocity?

a) 30 thou/s

b) xv m/southward

c) - ten m/s; five = v_i + a t = twenty chiliad/s + ( - 10 m/s2) (iii s) = (20 - 30) m/south = - 10 m/s

d) -- 30 m/south

9. Consider a brawl that is thrown straight upwards at the border of a coulee with an initial velocity of 20 m/s. Three seconds later, where is it located? Take its initial position, at the border of the coulee, to be the origin; that is, y_i = 0.

a) xxx m

b) 15 m; y = y_i + half dozen t + (¹/₂) a t² = 0 + (20 m/s) (3 south) + (¹/_ii) (- 10 m/s²) (3 s)² = (0 + 60 - 45) m = 15 m

c) - 10 thousand

d) - 30 m

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(C) 2003 Doug Davis, all rights reserved

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