Aspacecraft drifts through space at a constant velocity. suddenly a gas leak in the side of the spacecraft causes it to constantly accelerate in a direction perpendicular to the initial velocity. the orientation of the spacecraft does not change, so the acceleration remains perpendicular to the original direction of the velocity. what is the shape of the path followed by the spacecraft?

Here space craft is moving with constant velocity

Now due to gas leakage it will have acceleration perpendicular to velocity

it is given that acceleration is always perpendicular to velocity

So it will neither increase nor decrease the velocity

it will only change the direction of the motion

so it is the centripetal acceleration of the space craft

in this case we will say that path of the space craft will be circular path

So it will perform Uniform Circular Motion and its path will be a circle

see earlier