• 2: separation distance is 0.70 m.
  

• 2: f = 5.5 x 10¹⁴ Hz.
• 6: f = 0.2 Hz, v = 4.0 m/s.
• 40: Distance = 7.58 km
• 54: 800 seconds
• 74: 0.031
• 86: a) 194 m/s
  b) 2.59 x 10^-4 Hz.
  c) 3866 seconds
• 94: 123 dB
• 100: 79,400 people

• 2: 1.29 x 10²¹ molecules of Tyelenol.
  5.84 x 10²⁰ molecules of Advil.
• 10: temperature = 304K, or 31^oC
• 22: V_top/V_bottom = 1.02

• 12: 3.1 x 10^-5kg/s of ice melts.
• 18: filament area = 2.56 x 10^-5 m²
• 20: temperature = 5798K

• 56: Q=3.94 x 10⁵J, from evaporation of 0.163 kg of sweat.
• 80: final temperature = 63.9^oC

• 1: so it would be a square 17.8 m on a side
• 24: max depth = 0.5 m
• 50: 8.13 x 10⁶gal/day
• 58: P₁-P₂=96 N/m²

• 2: x=0.218 m
• 24: energy= 46.9 J, v=56 m/s
• 40: This is just 1/4 of a period, and T=1.62 s, so T/4=0.405 s
• 52: Stress = F/A = 1.7 x 10⁸N/m²,
  Strain=delta L/Lo=F/AY= 1.81 x 10^-2
• 58:(a) Strain = 2.5 x 10^-4 (b) 7.46 x 10^-5m

• 2: 210 N
• 6a: 13,500 Nm, 6b: 82,500 Nm
• 12: 0.7 m
• 18: 1200 N
• 34: torque=8 x 10^-4Nm
• 48: 7.67 m/s
• 52: 7.1 rad/s

• 2: 20.7 radians (note that 330 rev/min = 5.5 rev/s=34.6 rad/s)
• 6: 8.0 seconds
• 18: 5.22 seconds
• 20: It has rotated through an angle of 4,600 radians, while undergoing an angular acceleration of 200 rad/s
• 36: 6.53 rad/s²

• 12: total momentum = 322 kg m/s at 15.7 degrees north of east.

• 8: Work by push = 1050 J, work by friction = -943 J
• 14: v = 39.5 m/s
• 60: power = 4,000 W on the flat, and power = 33,400 W on the hill.

• 2: 0.792 m/s²
• 10: 10,570 revolutions per minute. Note it is going 0.3142 m/rev and 3320 m/min
• 20: 23^o
• 30: T = time for one orbit = 2.38 x 10⁶sec = 27.5 days
• 52: at equator a_c=0.0337 m/s², at 30^o latitude a_c= 0.0292 m/s²

• 14: 1.39 MN
• 20: a=4.24 m/s²
• 30: F_sun/F_moon=178
• 50: 4,257 N
• 58: T₁=919 N, T₂=845 N

• 6: v_x=10.7 m/s, v_y=13.2 m/s
• 14: v_horizontal=constant=8.6 m/s
• 26: 0.842 m

• 2: (a) 7.07 km (b) 2.12 km NE
• 6: el-Guerrouj wins by 109 meters
• 16: a) north, b) 7.13 m/s
• 28: 96.9 m/s
• 44: a) final v = 7.88 m/s downward, b) 3.165 m above the water.
• 68: 1.08 s

Math Review Sheet

• 1a: x⁸, 10⁴, 5x10^-5, 10, 3 x 10^-6
• 1b: 3.26 x 10⁴, 8.31 x 10^-1, 2 x 10^-4, 1.006 x 10³, 1.9 x 10^-10
• 2a: angle=65 degrees, sides are 9.06 cm and 4.23 cm long
• 2b: AC = 31.8 m long, side AD = 24.7 m long
• 3: 120, -2 and 3/2, -50, 99.99, 4.1 x 10^-18, 0.0623
• 4: 0.00358 g, 0.0000023 g, 15.7 MN