978-0073380308 Chapter 2 Solution Manual Part 33

350 Solutions Manual

Problem 2.271

A golfer chips the ball on a ﬂat, level part of a golf course as shown. Letting

˛D23ı

,

ˇD41ı

, and the initial speed be

v0D6m=s

, determine the

x

and

y

coordinates of the place where the ball will land.

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Dynamics 2e 351

Problem 2.272

Relative to the cylindrical coordinate system shown, with origin at

O

, the radial and

´

coordinates of point

G

are

RDdC.L=2/ cos ˇ

and

´D.L=2/ sin ˇ

, respectively, where

dD0:5

m and

LD

0:6

m. The shaft

CD

rotates as shown with a constant angular velocity

!sD10 rad=s

, and the angle

ˇ

varies with time as follows:

ˇD

ˇ0sin.2!t/

, where

ˇ0D0:3 rad

,

!D2rad=s

, and

t

is time in

seconds. Determine the velocity and the acceleration of

G

for

tD3

s

(express the result in the cylindrical component system

.OuR;Ou✓;Ou´/

,

with Ou✓DOu´⇥OuR).

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352 Solutions Manual

P

R

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 353

Problem 2.273

An airplane is traveling at a constant altitude of

10;000 ft

, with

a constant speed of

450 mph

, within the plane whose equation is

given by

xCyD10 mi

and in the direction of increasing

x

. Find

the expressions for

Pr

,

P

✓

,

P



,

Rr

,

R

✓

, and

R



that would be measured

when the airplane is closest to the radar station.

Solution

The figure at the right shows the trace of the path of the airplane on the

xy

plane. Since the airplane is moving along a straight line with constant

354 Solutions Manual

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 355

Problem 2.274

A carnival ride called the octopus consists of eight arms that rotate about the

´

axis at the constant angular

velocity

P

✓D6rpm

. The arms have a length

LD22 ft

and form an angle



with the

´

axis. Assuming that



varies with time as

.t/ D0C1sin !t

with

0D70:5ı

,

1D25:5ı

, and

!D1rad=s

, determine

the magnitude of the acceleration of the outer end of an arm when achieves its maximum value.

Solution

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permission of McGraw-Hill, is prohibited.

356 Solutions Manual

Problem 2.275

A particle is moving over the surface of a right cone with angle

ˇ

and under the constraint that

R2P

✓DK

, where

K

is a constant. The

equation describing the cone is

RD´tan ˇ

. Determine the expressions

for the velocity and the acceleration of the particle in terms of

K

,

ˇ

,

´

,

and the time derivatives of ´.

Solution

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 357

Problem 2.276

Solve Prob. 2.275 for general surfaces of revolution; that is,

R

is no

longer equal to

´tan ˇ

, but is now an arbitrary function of

´

, that is,

RDf .´/

. The expressions you need to find will contain

K

,

f .´/

,

derivatives of

f .´/

with respect to

´

, and derivatives of

´

with respect to

time.

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358 Solutions Manual

Problem 2.277

In a racquetball court, at point

P

with coordinates

xPD35 ft

,

yPD16 ft

, and

´PD1ft

, a ball is imparted a speed

v0D90 mph

and a direction defined by the angles

✓D63ı

and

ˇD8ı

(

ˇ

is the

angle formed by the initial velocity vector and the

xy

plane). The

ball bounces off the left vertical wall to then hit the front wall of

the court. Assume that the rebound off the left vertical wall occurs

such that (1) the component of the ball’s velocity tangent to the

wall before and after rebound is the same and (2) the component of

velocity normal to the wall right after impact is equal in magnitude

and opposite in direction to the same component of velocity right

before impact. Accounting for the effect of gravity, determine the

coordinates of the point on the front wall that will be hit by the ball

after rebounding off the left wall.

Solution

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permission of McGraw-Hill, is prohibited.

of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the

permission of McGraw-Hill, is prohibited.