# Distance of jump and weight relation

I just have a maybe slightly popular question.

You know the ski jumping sports. A friend of mine asked me if the distance of the jumper and the body weight could be related, neglecting the air resistance and physiological differences.

In other words, if we apply the same force to two objects with different mass on a slide (like the ones in the ski jumping) which one will fall further or will they fall to the same spot?

• If you think this is a well known question then please Google it. BTW the official distance in ski jumping is corrected for the speed of wind, so air resistance/drag is not negligible if you want to answer a more practical question. – Rol Feb 15 '17 at 3:43
• How is the same force to be applied to two different masses? In practice there is an optimum mass for a ski jumper which is smaller than you may imagine. physics.stackexchange.com/a/231475/104696 – Farcher Feb 15 '17 at 8:33
• @Farcher thank you for the link. It gave me some answer. – user2207915 Feb 15 '17 at 13:03
• @Rol I didn't know air resistance has the important role, thank you for pointing it out. The first thing I did was googling it, but there were different theories and I didn't know which one to believe. Sorry if this was a repeated question. – user2207915 Feb 15 '17 at 13:06
• @user2207915 All right, then tell us your bit of research so that we can understand what didn't make you happy in each solution you found. I googled it too and was satisfied after reading mcasco.com/Answers/qa_sjsad.html. – Rol Feb 15 '17 at 13:50

I will try explain it simply.

In propagation on Earth we consider two things

1. Kinematics
2. Kinetics

Kinematics only deals with velocity, acceleration, distance and not on any factors. Whereas Kinetics deals with mass, K.E, Force, P.E, etc

Now, if we apply same forces on two body simultaneously then at first we have to deal with kinetic equation to get the initial velocity Simply,

F*s = ½mu²............. Equation 1

You will get initial velocity u from the equation.

And to calculate final velocity we now have to consider Newtons Kinematics equation

v²=u²+2as................ Equation 2

Buy from equation 1 we understand that initial velocity will be smaller if the mass is heavy.

So the final velocity would be smaller from equation 2.

Conclusion :-For the same FORCE on two different body there would be two different velocity.

If you're neglecting external force both would be accelerated along the slide w/ $gsin \theta$ They would have the same speed at the bottom, and hence their range will be equal.