# Two bodies are falling with negligible air resistance

Two bodies are falling with negligible air resistance, side by side, above a horizontal plane.
If one of the bodies is given an additional horizontal acceleration during its descent, it

1. has the vertical component of its velocity altered
2. strikes the plane at the same time as the other body
3. follows a hyperbolic path
4. has the vertical components of its acceleration altered
5. follows a straight line path along the resultant acceleration vector

I was thinking it might be either 1 or 4...but I'm not very sure...I don't think that the acceleration would be altered because it's constant? But can someone help me confirm that or help me understand the solution? The homework is due today.

Thanks.

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Applying a horizontal force to the object will alter it's acceleration in the horizontal plane, but not in the vertical one. It should still strike the ground at the same time, just farther away from the other object.

HallsofIvy
Homework Helper
That's the whole point of using "components" of vectors.

Adding a horizontal acceleration affects only the horizontal components of acceleration, velocity and position.

1. has the vertical component of its velocity altered
1. is false- only the horizontal component is altered.
2. strikes the plane at the same time as the other body
2. is true since the vertical component of the position function is not changed.
3. follows a hyperbolic path
3. is false: it follows a parabolic path
4. has the vertical components of its acceleration altered
4. is false. Again, only the vertical component is altered.
5. follows a straight line path along the resultant acceleration vector
5. is false- see 3 above.

2. is the only true statement.