How Do You Calculate the Net Force on a Ball in Flight?

[Panzer22]

1. A ball is flying through the air, and at a given point in the flight, the ball is submitted to a gravitational force: F(g) = 1,5 N [downwards] and air resistance: F(air) = 0,50 N [32° above the horizontal]. Calculate the net force on the ball.


2. F (nette) = m x a



3. I thought I might have to find the vertical and horizontal components of the air resistance, so I found:
sin32 x 0,5N = 0,26N = x
cos32 x 0,5N = 0,42N = y

I also tried calculating the mass of the ball, in case it might prove useful:
Fg = m x g
1,5N = 9,8m
0,153 kg = m

But after calculating these values, I'm at a loss of what to do next. How do you find out the net force without having the other force on the horizontal axis? How can I use this data to calculate the net force? The answer key in my book says it should be 1,3N [71° under the horizontal], but I have no idea how this answer was achieved. I would be grateful for any help in solving this problem.

 

[neutrino]

I thought I might have to find the vertical and horizontal components of the air resistance, so I found:
sin32 x 0,5N = 0,26N = x
cos32 x 0,5N = 0,42N = y

You have the x and y components interchanged.

How do you find out the net force without having the other force on the horizontal axis?

Why should it have a non-zero horizontal component?

How can I use this data to calculate the net force?

Think of it this way: "Downwards" is 270 degrees away from the positive x-axis. Can you find the components of the gravitational force now?

 

[Panzer22]

Why should it have a non-zero horizontal component?

If the ball is in movement, shouldn't the horixontal component be non-zero?

And what does it being 270 degrees away from the positive x-axis have to do with it?

 

[neutrino]

To find the net force just add the two force vectors. You know what their components are along each direction.

And what does it being 270 degrees away from the positive x-axis have to do with it?

I was just trying to show you that the horizontal component of the gravitational force is zero.