The formula V=(square root) 2GM/r
represents the relationship of the escape velocity, V, from the surface of the earth, the gravitational constant, G, the mass of the earth, M, and the radius of the earth, r. If G=6.67\times10^-11, m=5.98×10^24 kg, and r=6.38\times10^6, find v.
so just plug in your numbers.
v^2 = 2(6.67*10^-11)(5.98*10^24)(6.38*10^6)
= (2*6.67*5.98*6.38)*10^(-11+24+6)
= 508.953*10^19
= 50.8953*10^20
v = 7.134*10^10
My professor said that was a wrong answer and that it should be a 5-digit number so an integer between 10,000 and 99,999.
well, I can see my mistake.
I multiplied by r, instead of dividing.
Now you know how to fix it.
I got the answer 6877*10^20/5500. I'm not sure what I'm doing wrong here.
To find the escape velocity (V) from the surface of the Earth using the given formula V = √(2GM/r), we need to substitute the given values for the gravitational constant (G = 6.67 × 10^(-11) m^3 kg^(-1) s^(-2)), the mass of the Earth (M = 5.98 × 10^(24) kg), and the radius of the Earth (r = 6.38 × 10^(6) m).
Plugging in the values, the formula becomes:
V = √((2 × 6.67 × 10^(-11) m^3 kg^(-1) s^(-2) × 5.98 × 10^(24) kg) / (6.38 × 10^(6) m))
Simplifying the expression within the square root:
V = √((2 × 6.67 × 5.98 × 10^(13)) / (6.38))
Now, let's calculate V:
V = √(7.97 × 10^(14) / 6.38)
V = √(1.25 × 10^(14))
V ≈ 1.12 × 10^(7) m/s
Therefore, the escape velocity from the surface of the Earth is approximately 1.12 × 10^(7) m/s.