john and paul are trying to move a 100kg piano which is resulting on a flat, smooth floor. John pushing towards the North, while Paul is pushing towards the East. Both are exerting a 100N force. What is acceleration of the piano (magnitude and direction)?

Question

A=200/100=2m/s^2

Answer 1

45 North East

110^2+100^2=20,000

Sqrt*(20,000)=141N

141N=m*a

141N=100kg*a

141N/100kg=a

a=1.41m/s^2

Answer 2

Direction:

45 North East

110^2+100^2=20,000

Magnitude:

Sqrt*(20,000)=141N

Acceleration:

141N=m*a

141N=100kg*a

141N/100kg=a

a=1.41m/s^2

Answer 3

45 North East

110^2+100^2=20,000

Sqrt*(20,000)=141N

Not sure how you came up with 45NE and 110? Did you add force of gravity?

Answer 4

Trish,

Its vector addition:

--->
^
I
I
I

Spacing is a problem on this form. But one vector is pointing up (north) and the other is pointing to the right (east). Intuitively, you should be able to see which way the resultant vector will point. However, you may want to go over or google head to tail method, to see which way the resultant vector will point. Since magnitudes are equal, you should already know that the resultant angle will be between the north and east vector.

I have a typo: it should read 100^2+100^2=20,000 and not 110^2+100^2=20,000

The math is based on the Pythagorean theorem.

x^2+y^2=r^2 or 110^2+100^2=20,000

Solving for r:

r=sqrt*(x^2+y^2)