- #1
newjerseyrunner
- 1,533
- 637
I want to know how fast the space shuttle would have to hit the Earth to unleash the same kinetic energy as the asteroid that killed the dinosaurs. I've already determined that it's relativistic, by showing that Newtonian physics gives a v greater than c
But once I plug in the equations, I get a wrong result.
KE = (m * c ^ 2) / sqrt(1 - (v ^ 2 / c ^ 2))
KE / (m * c ^ 2) = sqrt(1 - (v ^ 2 / c ^ 2))
((KE / (m * c ^ 2)) ^ 2) - 1 = -(v ^ 2 / c ^ 2)
v = -sqrt((((KE / (m * c ^ 2)) ^ 2) - 1) * c ^ 2)
KE = 4.2e25J
c = 1
m = 2e6kg
v = -sqrt((((4.2e25 / (2e6)) ^ 2) - 1) * 1)
v = -2.1e+19
I'm expecting an answer between 0 and 1, where did I go wrong?
4.2e25J = (2e6 * v ^ 2 ) / 2.
8.4e25J = 2e6 * v ^ 2
v = sqrt(8.4e25J / 2e6)
v = 6,480,740,698 m/s
8.4e25J = 2e6 * v ^ 2
v = sqrt(8.4e25J / 2e6)
v = 6,480,740,698 m/s
KE = (m * c ^ 2) / sqrt(1 - (v ^ 2 / c ^ 2))
KE / (m * c ^ 2) = sqrt(1 - (v ^ 2 / c ^ 2))
((KE / (m * c ^ 2)) ^ 2) - 1 = -(v ^ 2 / c ^ 2)
v = -sqrt((((KE / (m * c ^ 2)) ^ 2) - 1) * c ^ 2)
KE = 4.2e25J
c = 1
m = 2e6kg
v = -sqrt((((4.2e25 / (2e6)) ^ 2) - 1) * 1)
v = -2.1e+19
I'm expecting an answer between 0 and 1, where did I go wrong?