Finding Horizontal Displacement of a Dropped Cup on an Accelerating Airplane

[nick227]

Homework Statement

A cup of coffee is dropped aboard an airplane accelerating along a smooth runway. If it falls a vertical distance of 1.0 meter, find its horizontal displacement when it hits the floor. Assume a constant horizontal acceleration of 1.5m/s^2 for the airplane.

Homework Equations

F=ma

The Attempt at a Solution

This chapter is about noninertial reference systems, if that means anything for this problem.

I looked at the problem and said there was a force due to gravity and a force from the horizontal acceleration.

f=ma=mg+ma1

v(dv/dx)=g+a1

I don't think I started this correctly, because we don't have a velocity. Am I going in the right direction here?

 

[CompuChip]

f=ma=mg+ma1

So suppose you have this. Now write a = dv/dt (I don't see how you managed to get v dv/dx) and integrate both sides.

Note however, that you should not just add the accelerations! They have different directions and therefore you should add them as vectors. Write out the acceleration in the horizontal and vertical direction separately. Then you can solve for the horizontal and vertical velocity and vector-add them to get the velocity vector. Or you can use just the horizontal velocity to find the horizontal displacement (you will need the other one as well though, since there will still be information missing you can only extract from the vertical component).