Answer:
73.6 minutes
Explanation:
relative time = time interval / √(1 - observer velocity² / speed of light²)
we have relative time. we want time interval.
rearrange
time interval = relative time x √(1 - observer velocity² / speed of light²)
convert 85 mins into seconds
85 x 60 = 5100
1.5 x 10⁸ as a number is 150000000
for c = 299 792 458
time interval = 5100 x √(1 - 150 000 000² / 299 792 458²)
for c = 3 x 10⁸
time interval = 5100 x √(1 - 150 000 000² / 300 000 000²)
time interval = 5100 x 0.866
time interval = 4415.71
divide by 60 for back into minutes
time = 73.6 minutes
Answer:
6.86 × 10²⁴ kg
Explanation:
The mass of the earth m = density of earth, ρ × volume of earth, V
m = ρV
The density of the earth, ρ = 5515 kg/m³ and since the earth is a sphere, its volume is the volume of a sphere V = 4πr³/3 where r = radius of the earth = 6.67 × 10⁶ m
Since m = ρV
m = ρ4πr³/3
So, substituting the values of the variables into the equation for the mass of the earth, m, we have
m = 5515 kg/m³ × 4π(6.67 × 10⁶ m)³/3
m = 5515 kg/m³ × 4π × 296.741 × 10¹⁸ m³/3
m = 5515 kg/m³ × 1189.9639π × 10¹⁸ m³/3
m = 6546105.64378π × 10¹⁸ kg/3
m = 20565197.400122 × 10¹⁸ kg/3
m = 6855065.8 × 10¹⁸ kg
m = 6.8550658 × 10²⁴ kg
m ≅ 6.86 × 10²⁴ kg
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Apply the combined gas law
PV/T = const.
P = pressure, V = volume, T = temperature, PV/T must stay constant.
Initial PVT values:
P = 1atm, V = 8.0L, T = 20.0°C = 293.15K
Final PVT values:
P = ?, V = 1.0L, T = 10.0°C = 283.15K
Set the PV/T expression for the initial and final PVT values equal to each other and solve for the final P:
1(8.0)/293.15 = P(1.0)/283.15
P = 7.7atm
