Physics
posted by Jordan Stark .
A spaceship and its occupants have a total mass of 170000kg . The occupants would like to travel to a star that is 31 lightyears away at a speed of 0.40c. To accelerate, the engine of the spaceship changes mass directly to energy.
How much mass will be converted to energy to accelerate the spaceship to this speed? Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.40c, and ignore decrease in total mass for the calculation.

Compute the increase in kinetic energy desired. Divide that by c^2 for the mass loss required.
You will be accurate enough if you use (1/2) M V^2 for the kinetic energy required. For V, assume 0.4c
Delta M = (1/2) M V^2/c^2 = (1/2)M*0.16c^2/c^2
= 0.08 M
You don't need to use the 31 light year distance. 
I tried that and it didn't work at all