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If I have a blow of force N that strikes an object and launches that object of weight W at angle A into the air moving said object a distance D from where it was struck.

What other considerations (efficiency of energy transfer?) and formula can I use to determine what N is if I know A, D and W?

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From the information that you have got you can find the impulse $\displaystyle \int F (t) \, dt$ over the period for which the force was acting.
What you need to find is the time interval over which the force was acting and how the force was changing during that time interval which is usually quite a difficult thing to do without specialised apparatus.

There are devices which measure the force as a function of time directly and here is a description of an experiment, Measuring Impulse and Momentum Change in 1 Dimension, which uses such a device.

In terms of your measured projectile motion you would have to consider the effect of air resistance.

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  • $\begingroup$ So the impulse is equal to the amount of force transferred to the object (causing it to fly through the air) ? $\endgroup$
    – Rob
    Commented Jan 24, 2019 at 9:55
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    $\begingroup$ @Rob Impulse is equal to the change in momentum . $\endgroup$
    – Farcher
    Commented Jan 24, 2019 at 9:57

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