1. Approximately 31.5 s

3. $400/(\ln 2)\approx 577ft$

5. $400\ln 7\approx 778ft$

7. (a) 100 ft/sec; (b) about 23 sec and 1403 ft to reach 90 ft/sec

8. (a) 100 ft/sec; (b) about 14.7 sec and 830 ft to reach 90 ft/sec

9. 50 ft/s

10. About 5 min 47 s

11. Time of fall: about 12.5 s

12. Approximately 648 ft

19. Approximately 30.46 ft/s; exactly 40 ft/s

20. Approximately 277.26 ft

22. Approximately 20.67 ft/s; about 484.57 s

23. Approximately 259.304 s

24. (a) About 0:88 cm; (b) about 2:91 km

25. (b) About 1.389 km/sec; (c) $r_{\text{max}}=100R/19\approx 5.26R$

26. Yes

28. (b) After about $8\frac{1}{2}$ minutes it hits the surface at about 4.116 km/sec.

29. About 51.427 km

30. Approximately 11.11 km/sec (as compared with the earth’s escape velocity of about 11.18 km/sec).