Question

Question: -A spacecraft drifts through space at a constant velocity. Suddenly, a gas leak in the side of the spacecraft gives it a constant acceleration 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 in this situation?

Short answer

The spacecraft follows a parabolic path.

Step-by-step solution

The definition of a projectile

A projectile is a body that is projected at an angle to the horizontal plane, only under the influence of gravity.

The shape of the path followed by the spacecraft

The spacecraft takes a parabolic route, similar to a projectile launched from a cliff with a horizontal velocity. Gravity delivers acceleration to the projectile that is always perpendicular to its initial velocity, resulting in a parabolic path. The beginning velocity of the spacecraft, on the other hand, is the similar to the horizontal velocity of the projectile, and the leaking of the gas is the same as gravity in the case of the projectile.

Gravity, which acts in a perpendicular direction to the initial velocity, provides the acceleration in the case of a projectile. In such instances, the projectiles follow a parabola's path.

As a result of the preceding paragraph, the spacecraft will follow a parabolic route.