VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS
VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS
12th Edition
ISBN: 9781260265521
Author: BEER
Publisher: MCG
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Textbook Question
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Chapter 11.1, Problem 11.29P

The acceleration due to gravity at an altitude y above the surface of the earth be expressed as
   a = 32.2 [ 1 + ( y / 20.9 × 10 6 ) ] 2 where a and y are expressed in ft/s2 and feet, respectively. Using this expression, compute the height reached by a projectile fired vertically upward from the surface of the earth if its initial velocity is (a) 1800 ft/s, (b) 3000ft/s, (c) 36,700 ft/s.

  Chapter 11.1, Problem 11.29P, The acceleration due to gravity at an altitude y above the surface of the earth be expressed as

Expert Solution
Check Mark
To determine

To calculate:

The height reached by a projectile fired vertically upward from the surface of the earth if its initial velocity is 1800 ft/s.

Answer to Problem 11.29P

If the initial velocity is 1800 ft/s, the maximum height reached is 50,431.96 ft.

Explanation of Solution

Given information:

The acceleration due to gravity at an altitude y above the surface of the earth can be expressed as a=32.2[1+(y20.9×106)]2 where a and y are expressed in ft/s2 and feet, respectively.

VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS, Chapter 11.1, Problem 11.29P

Concept used:

Substitute a=vdvdy to the equation a=32.2[1+(y20.9×106)]2 and integrate to find a relation between displacement and velocity.

Calculation:

a=32.2[1+(y20.9×106)]2

vdvdy=32.2[1+(y20.9×106)]2

v dv=32.2[1+(y20.9×106)]2 dy

v22+k=672.98×106[1+(y20.9×106)]1; Here k is a constant.

Let v=v0 when y=0;

v022+k=672.98×106[1+0]1

k=v022+672.98×106

Therefore, the equation can be written as;

v22v022+672.98×106=672.98×106[1+(y20.9×106)]1; where v0 is the initial velocity.

Calculate the maximum height the projectile will reach; when this happens v=0.

v22v022+672.98×106=672.98×106[1+(y20.9×106)]1

v022+672.98×106=672.98×106[1+(y20.9×106)]1

[1+(y20.9×106)]1=[1(v021345.96×106)](1)

When v0=1800 ft/s2; using equation (1);

[1+(y20.9×106)]1=[1(180021345.96×106)]

y=50,431.96 ft

Conclusion:

If the initial velocity is 1800 ft/s, the maximum height reached is 50,431.96 ft.

If the initial velocity is 3000 ft/s, the maximum height reached is 140,692.32 ft.

Expert Solution
Check Mark
To determine

To calculate:

The height reached by a projectile fired vertically upward from the surface of the earth if its initial velocity is 3000 ft/s.

Explanation of Solution

Calculation:

When v0=3000 ft/s2; using equation (1) in sub part (i);

[1+(y20.9×106)]1=[1(300021345.96×106)]

y=140,692.32 ft

Conclusion:

If the initial velocity is 3000 ft/s, the maximum height reached is 140,692.32 ft.

Expert Solution
Check Mark
To determine

To calculate:

The height reached by a projectile fired vertically upward from the surface of the earth if its initial velocity is 36700 ft/s.

Answer to Problem 11.29P

When projected at 36,700 ft/s, the projectile will escape the gravitational pull of the earth.

Explanation of Solution

Calculation:

Consider equation (1) in sub part (i);

[1+(y20.9×106)]1=[1(v021345.96×106)](1)

Rearrange the equation;

[1+(y20.9×106)]=1[1(v021345.96×106)]

When the right hand side denominator is zero, y will reach an infinite value. Find v0 such that the left hand side numerator is zero.

1(v021345.96×106)=0

v0=1345.96×10636687.33 ft/s

Therefore, when the projectile has an initial velocity greater than or equal to 36687.33 ft/s, the projectile will escape the gravitational pull of the earth.

Hence, when projected at 36,700 ft/s, the projectile will escape the gravitational pull of the earth.

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Chapter 11 Solutions

VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS

Ch. 11.1 - The brakes of a car are applied, causing it to...Ch. 11.1 - The acceleration of a particle is defined by the...Ch. 11.1 - The acceleration of a particle is defined by the...Ch. 11.1 - Many car companies are performing research on...Ch. 11.1 - A Scotch yoke is a mechanism that transforms the...Ch. 11.1 - For the Scotch yoke mechanism shown, the...Ch. 11.1 - A piece of electronic equipment that is surrounded...Ch. 11.1 - A projectile enters a resisting medium at x=0 with...Ch. 11.1 - Point A oscillates with an acceleration...Ch. 11.1 - A brass (nonmagnetic) block A and a steel magnet B...Ch. 11.1 - Based on experimental observations, the...Ch. 11.1 - A spring AB is attached to a support at A and to a...Ch. 11.1 - The acceleration of a particle is defined by the...Ch. 11.1 - Starting from x=0 with no initial velocity, a...Ch. 11.1 - A ball is dropped from a boat so that it strikes...Ch. 11.1 - The acceleration of a particle is defined by the...Ch. 11.1 - The acceleration of a particle is defined by the...Ch. 11.1 - A human-powered vehicle (HPV) team wants to model...Ch. 11.1 - Experimental data indicate that in a region...Ch. 11.1 - Based on observations, the speed of a jogger can...Ch. 11.1 - The acceleration due to gravity at an altitude y...Ch. 11.1 - The acceleration due to gravity of a particle...Ch. 11.1 - The velocity of a particle is v=v0[1sin(t/T)] ....Ch. 11.1 - An eccentric circular cam, which serves a similar...Ch. 11.2 - An airplane begins its take-off run at A with zero...Ch. 11.2 - A minivan is tested for acceleration and braking....Ch. 11.2 - Steep safety ramps are built beside mountain...Ch. 11.2 - A group of students launches a model rocket in the...Ch. 11.2 - A small package is released from rest at A and...Ch. 11.2 - A sprinter in a 100-m race accelerates uniformly...Ch. 11.2 - Automobile A starts from O and accelerates at the...Ch. 11.2 - In a boat race, boat A is leading boat B by 50 m...Ch. 11.2 - As relay runner A enters the 65-ft-long exchange...Ch. 11.2 - Automobiles A and B are traveling in adjacent...Ch. 11.2 - Two automobiles A and B are approaching each other...Ch. 11.2 - An elevator is moving upward at a constant speed...Ch. 11.2 - Two rockets are launched at a fireworks display....Ch. 11.2 - Car A is parked along the northbound lane of a...Ch. 11.2 - The elevator E shown in the figure moves downward...Ch. 11.2 - The elevator E shown starts from rest and moves...Ch. 11.2 - An athlete pulls handle A to the left with a...Ch. 11.2 - An athlete pulls handle A to the left with a...Ch. 11.2 - In the position shown, collar B moves to the left...Ch. 11.2 - Collar A starts from rest and moves to the right...Ch. 11.2 - A farmer lifts his hay bales into the top loft of...Ch. 11.2 - The motor M reels in the cable at a constant rate...Ch. 11.2 - Collar A starts from rest at t=0 and moves upward...Ch. 11.2 - Collars A and B start from rest, and collar A...Ch. 11.2 - Block B starts from rest, block A moves with a...Ch. 11.2 - Block B moves downward with a constant velocity of...Ch. 11.2 - The system shown starts from rest, and each...Ch. 11.2 - The system shown starts from rest, and the length...Ch. 11.3 - A particle moves in a straight line with a...Ch. 11.3 - A particle moves in a straight line with a...Ch. 11.3 - A particle moves in a straight line with the...Ch. 11.3 - Prob. 11.64PCh. 11.3 - Prob. 11.65PCh. 11.3 - A parachutist is in free fall at a rate of 200...Ch. 11.3 - A commuter train traveling at 40 mi/h is 3 mi from...Ch. 11.3 - Prob. 11.68PCh. 11.3 - In a water-tank test involving the launching of a...Ch. 11.3 - Prob. 11.70PCh. 11.3 - Prob. 11.71PCh. 11.3 - A car and a truck are both traveling at the...Ch. 11.3 - Solve Prob. 11.72, assuming that the driver of the...Ch. 11.3 - Car A is traveling on a highway at a constant...Ch. 11.3 - An elevator starts from rest and moves upward,...Ch. 11.3 - Car A is traveling at 40 mi/h when it enters a 30...Ch. 11.3 - An accelerometer record for the motion of a given...Ch. 11.3 - Prob. 11.78PCh. 11.3 - An airport shuttle train travels between two...Ch. 11.3 - Prob. 11.80PCh. 11.3 - Prob. 11.81PCh. 11.3 - The acceleration record shown was obtained during...Ch. 11.3 - A training airplane has a velocity of 126 ft/s...Ch. 11.3 - Shown in the figure is a portion of the...Ch. 11.3 - An elevator starts from rest and rises 40 m to its...Ch. 11.3 - Prob. 11.86PCh. 11.3 - Prob. 11.87PCh. 11.3 - Prob. 11.88PCh. 11.4 - Two model rockets are fired simultaneously from a...Ch. 11.4 - Ball A is thrown straight up. 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