If you run at 1.7 m/s FORWARD ,how does this affect the speed of a ball that you throw?

We have a problem about conservation and velocity, we will find that it does affect the speed of the ball, increasing it by 1.7m/s.

There is something called momentum, which we can define as the "quantity of movement", and we can simply write as the product between velocity and mass.

The momentum is conservative, then we have conservation of momentum.

This means that when you run whit the ball in your hands, the momentum of the ball will be equal to your velocity times the mass of the ball, and this must conserve after you throw the ball.

Now with this idea in mind, this means that if you run with a velocity V, and you throw the ball with a velocity V', the velocity of the ball when it leaves your hand will be:

V + V'.

So, if you run with a velocity of 1.7m/s forward and you throw the ball (assuming in the same direction) the speed of the ball will be 1.7m/s larger than if you were to throw it standing still.

If you want to learn more, you can read:

f is prop to m1xm2 double m1 double force