1. a. The lander is descending and slowing. The acceleration vector points upward, and so $\vec{F}{}_{\text{net}}$ points upward. This can be true only if the thrust has a larger magnitude than the weight.

2. a. You are descending and slowing, so your acceleration vector points upward and there is a net upward force on you. The floor pushes up against your feet harder than gravity pulls down.

3. $f_B>f_C=f_D=f_E>f_A$. Situations C, D, and E are all kinetic friction, which does not depend on either velocity or acceleration. Kinetic friction is smaller than the maximum static friction that is exerted in B. $f_{\text{A}}=0$ because no friction is needed to keep the object at rest.

4. d. The ball is shot down at 30 m/s, so $v_{0y}=-30\text{m}\text{/}\text{s}$. This exceeds the terminal speed, so the upward drag force is larger than the downward weight force. Thus the ball slows down even though it is “falling.” It will slow until $v_y=-15\text{m}\text{/}\text{s}$, the terminal velocity, then maintain that velocity.

1. $94\text{N,}58\text{°}$ below the horizontal

3. 147 N

5. 510 N

7. 800 N

9. $a_x=1.5\text{m}\text{/}{\text{s}}^2\text{,}{a}_y=0\text{m}\text{/}{\text{s}}^2$

11. $12\text{N}î\text{,}0\text{N}î\text{,}-6\text{N}î$

13.

1. 490 N

2. 490 N

3. 740 N, 240 N

15. 40 s

17.

1. 540 N

2. $m=55\text{kg; }mg=210\text{N}$

19. 0135 N, 740 N, 590 N

21.

1. $5.2\text{m}\text{/}{\text{s}}^2$

2. $1.0\times {10}^3\text{kg}$

23. $0.024{\text{m/s}}^2$

25. 0.250

27. 9 m/s

29.

1. $2.5\text{m}\text{/}{\text{s}}^2$

2. $2.3\text{m}\text{/}{\text{s}}^2$

31. 25 m/s

33.

1. $0.33\text{m}\text{/}\text{s}$

2. 5.0 mm/s

35.

1. 32 s

2. 7.7 h

37. $21\mu \text{m}\text{/}\text{s}$

39. 6400 N, 4380 N

41. $-3.2\text{m}\text{/}\text{s}$

43. 59 N

45.

1. 6700 N

2. $600\mu s$

47.

1. $v\left(h\right)=\sqrt{2\left({\displaystyle \frac{F_{\text{thrust}}}{m}}\right)h}$

2. 54 m/s

49.

1. 16.9 m/s

2. 229 m

51.

1. 4.5 m

2. 8.8 m/s

53. 0.49

55. $d_{\text{min}}={\displaystyle \frac{v^2{}_0}{2({\mu }_{\text{S}}g)}}$

57. Stay at rest

59.

1. 0 N

2. 220 N

61.

1. ${\displaystyle \frac{F_0}{m}}{\displaystyle \frac{T}{2}}$

2. ${\displaystyle \frac{F_0}{m}}{\displaystyle \frac{T^2}{3}}$

63.

1. $-5g$

2. $3g$

65. 69 g

67. $16\text{m}\text{/}\text{s}$

69.

1. $v=v_0{e}^{-6\pi \eta rt/m}$

2. 0.20 s

71.

3. 102 m

73.

3. $2.8\text{m}\text{/}{\text{s}}^2$

75.

2. $v_1=\sqrt{{\displaystyle \frac{k}{m}}}L$

77.

1. $v=v_0{e}^{-6\pi \eta t/m}$

2. 0.20 s

79.

2. 160 s, 480 s