1.16. tm = vil'± v212
vf
'
1.17. C D = I ji — 1.
1.18. See Fig. lb.
1.19.' (a) (v)
aR/T = 50 cm/s; (b) 1(v)1 = 2R/r = 32 cm/s;
(c) j(w)1 = 2nR/T2 = 10 cm/s2.
1.20. (a) v = a(1 — 2at), w = —2aa = const; (b) At = 1/a,
s = a/2a.
1.21. (a) x = vot (1 —t/2t), x =0.24, 0 and — 4.0 m;
(1 — t/a) vot for t -
<__T,
24
[1 4- (1 —
2] vot/2 for
4 and 34 cm respectively.
(b) 1.1, 9 and 11 s;
(0) s =
0-0
1.22. (a) v = a2t/2, w = a2/2; (b) (v).= a V- s-/2.
1.23. (a) s = (2/3a) vo/2; (b) t = 2V 1 '01 a.
1.24. (a) y = —x 2b1a2; (b) v = ai — 2btj, w = --2bj, v
1 1 a2 46 ,20
= 2b; (c) tan a = al2bt; (d) (v) = ai —btj, 1(0 =
= Va2 + b2t2.
1.25. (a) y = x — x2a/a; (b) v = a -V 1 + (1 — 2at)2, w = 2aa
= const; (c) to = 1/a.
1.26. (a) s= aorr; (b)
1.27. vo = (1+ a2) w/2b.
1.28. (a) r = v
°
t
gt2/2; (b) (v )t = gcos a
= vo
gt/2, (v) = vo — g (vog)/g2 •
ysin
1.29. (a) i = 2 (vo/g) sin a;
(b) h= (vV2g) sin2 a, / = (v2 o /g) sin 2a,
= 76';
r/2
z t
(c) y = x tan a — (g/24 cost a) x2;
-11 sin a
(d) R-, = g cos a, R2 = (vV g) cost a.
1.30. See Fig. 2.
1.31. / = 8h sin a.
1.32. 0.41 or 0.71 min later, depending on the initial angle.
2vo
sin (01 — 02)
1.33. At =
=11 s.
g cos 01 + cos 02
1.34. (a) x = (a/2V 0) y2;
(b) iv = avo, w-r = a2Y
(aY/vo)2'
wn = avo/V I + (ay/vo) 21.35. (a)
y = (b12a) x2;
(b)
R = v 2/w7, = v2141 w2
= (alb) [1 + (xbla)9 3/2.
1.36. v = y 2ax.
1.37. w= a V 1+ (43trt)2 = 0.8 m/s2.
1.38. (a) v = vo/(1
vot/R) = v fi e -81R; (b) w= v 2 41Re2s/n=- -
=- y2v2/R.
1.39. tan a = 2s1 R.
1.40. (a) wo = a26)2 I R = 2.6 m/s2, wa = aa)2 = 3.2 m/s2; (b) Wm in
ao)2 V 1 — (R/2a)2 = 2.5 m/s2, lm = ± a V 1 — R2/2a2 = ± 0.37 m.
lmrn —
1
1
v2-12vi
l v? +
Fig. 2.
282