Last revised 1999/09/27 |
4-69.
ac = 4 pi2 R cos(latitude) / (1 day)2 = 0.03 m / sec2,
where R is the radius of the earth.
4-91.
(a) The speed of our galaxy as seen from Galaxy A is 0.35 c.
(b) The speed of Galaxy B as seen from Galaxy A is 0.62 c, not 0.70 c .
Sheet # V.
(a) The man should row at an angle given by
sin (theta) = - vrowing / ( vwalking + vwater)
provided that vwalking > ( vrowing2 - vwater2 ) / vwater ; otherwise sin(theta)=- vwater / vrowing .
The angle is defined relative to a line directed straight across the river; positive angles point downstream.
(b) The trip takes
T = w [ vwalking + vwater + vrowing sin (theta) ] / [ vrowing vwalking cos (theta) ]
= w sqrt [ (1 / vrowing)2 (1 + vwater / vwalking )2 - (1 / vwalking)2 ]
where w is the width of the river.
Sheet # VI.
(a) t = sqrt ( 2 pi r / b )
(b), (c) v = sqrt ( 2 b pi R ) downward
(d)
ac = - 2 pi b
atangential = - b
(e)
The magnitude of the total acceleration is a = b sqrt( 4 pi2 + 1 )
The angle is given by tan (theta) = pi + [1 / (2 pi)] , measured from the positive x-axis.
Sheet # VII.
(a) The path will be an ellipse.
(b) v = omega [ x0 cos (omega t) 1x - y0 sin (omega t) 1y ]
(c) a = - (omega)2 r
(d) The velocity is a maximum or minimum whenever x = 0 or y = 0
= 0.86 m/sec2 1x - 0.16 m/sec2 1y
= 0.88 m/sec2, 11o below the x axis
[numbers from an previous edition of HRW]
5-11. [HRW answers]
(a) a = 0 [Forces in -x direction]
(b) a = 0.83 m/sec2 1x [Forces in the -x direction]
(c) a = 0 [Forces at 34o above and below the -x direction]