You have been provided a header $2$DMotion.h$,$ which you may change as you like. However,

you must implement all the functionality used by the provided test harness file a$3$q$2.$cc$,$ as

that file $($or a similar one in how it uses the Point and Force classes$)$ will be used to test

your program. You may not change the test harness, as we will test you with our own copy

of it$,$ so any changes you make won$$t be reflected in how your solution is tested! You must

implement the following functions for this question:

$$ Point default constructor. Should initialize both x and y to $0.$

$$ Force default constructor. Should initialize both angle and magnitude to $0.$

$$ An overloaded input operator for Point objects. Should read in first the x field, then

the y field.

$$ An overloaded input operator for Force objects. Should read in first the angle, then

the magnitude.

$$ An overloaded output operator for Point objects. Should print them out in the format:

$(,)($Note is used to denote that the variables value should go

there, so if the point has x value $4,$ and y value $5,$ you should print out $(4,5).$

$$ An overloaded output operator for Force objects. Should print them out in the format:

$$ degrees with magnitude of $$

$$ An overloaded addition operator between a Point object and a Force object. This

should effectively create a new Point that is the result of $$moving$$ the original by that

Force. This requires a bit of trigonometry! You will require the header, and

should use the PI constant defined in the provided $2$DMotion.h file. In order move a

Point by a given Force you must determine the horizontal and vertical components

of the given Force. Doing so is simple trigonometry. Consider that the magnitude of

a Force is simply the hypotenuse of a right$-$angle triangle. Given the hypotenuse and

angle of a right$-$angle triangle you can easily find out the length of the other sides $($the

horizontal and vertical components$)$ using sin and cos provided in the library

$-$ but be wary, those operations work on radians!

$$ An overloaded multiplication operator between a Force and an int scalar. This should

simply produce a new Force which has a magnitude scaled by the given scalar.

$$ int Point::quadrant$()-$ A member function that returns the quadrant $(1,2,3,$ or $4)$

that the given point is in$.$ See quadrants in diagram above.

A test harness is provided in the file a$3$q$2.$cc$.$ Make sure to read and understand this

code, as you will need to know what it does in order to structure your test suite.

The test harness has commnets describing the commands