Find a general expression for time of impact of a paper plane

[peglegmeg152]

Homework Statement

Two students threw a paper plane towards the bin, hitting a desk at time t=10. The trajectory can be modeled as follows:

x=t-2sin(t), y=4-3cos(t)

Then there were a few simple questions before:

The students are curious about what would have happened to the paper plane if it had not been obstructed. By repeating the trajectory for different lengths of impact (e.g. 10 metres, 20 metres etc.) find a general expression to indicate the time of impact of the plane for student heads at 10 metre intervals.

Homework Equations

x=t-2sin(t), y=4-3cos(t)

The Attempt at a Solution

I found what y was when t=10, then found heaps of values for t when y was at that height (the height of the obstruction) using co-terminal angles… not sure whether this is right or not, but I have no idea what to do now.

Many thanks for any help.

 

[haruspex]

I found what y was when t=10, then found heaps of values for t when y was at that height

I believe the question is asking for the times at which the horizontal distance traveled will be 10m, 20m etc. It bothers me that that makes the y coordinate irrelevant, but perhaps there were more parts to the question.
At first I thought it meant path lengths of 10m etc., but that makes it far too hard.