The main part of the problem and the graph is solved. The extra optional part is based on the answer and the context of Q2.

***Need help on the extra optional part on the bottom of the page. The main part of the problem and the graph is solved. The extra optional part is based on the answer and the context of Q2. The answer for Q2 is in the attached picture. Work and Hooke's Law

Q2.

You recently bought a compound bow and you decide to investigate its "spring like" properties to determine the initial launch speed of your arrows. You decide that the easiest way to measure the force required to displace the bowstring is to hang the bow from the ceiling and then pull down on the bowstring while standing on a scale. By drawing a free body diagram, you can find the relation between the force exerted by the bow string Fbow and the normal force from the scale (n). Using your bathroom scale, you collect the following measurements (assume your mass is 80 kg). By plotting the force as function of stretching you hope to estimate the amount of energy you have stored in the bow. You assume 80% of that energy will be given to the arrow (which you have measured to have a mass of M = 0.02 kg).

Extra Optional: If you aim the arrow directly horizontal and shoot at a target a distance X = 30 meters away, how far above or below the bulls-eye (1 meter below the arrow's release height) will the arrow hit the target? (Neglect the Drag force from the air on the arrow.) [Solve first using variables and then calculate the numerical value.]

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