Chapter Text
Motivation for the Problem:
[Adapted from Chapter 98 of the Exiled Rebels GDC translation]
On the other hand, Jin Ling saw an entire courtyard of arrows aimed at him as soon as he arrived. His pupils shrank. One of the monks had probably never seen Jin Ling before, or perhaps he had the determination to kill off any intruders. He let go, and an arrow shot towards the direction of Jin Ling!
As soon as he heard the sharp whistle, Wei WuXian knew that the archer was a skilled one. If Jin Ling were to be shot, his chest would be pierced through for sure. There was only one thing he could use to block it right now. Under the emergency, Wei WuXian leaped up the wall and casted something out, at the same time shouting, “Run, Jin Ling!”
What he flung out was the bamboo flute he’d been carrying with him ever since he was reborn. It blocked the brutal attack, and the arrow’s aim was off. The flute burst into pieces as well.
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Notes:
As everyone knows, fractions less than a hundredth do not exist in the MDZS universe. That being said, please round all your answers to two decimal places. If a problem requires you use an answer from a previous section, please use the rounded answer. After all, plot armor will take care of any round-off errors!
Assume g = 10 m/s^2.
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The Problem Itself:
According to records, a standard LanLingJin arrow is 75 cm long and has a mass of 15 grams.
1. Based on prior empirical knowledge and a healthy dose of handy-dandy guesstimation, Wei WuXian concludes the tension in the bowstring to be 500 newtons.
The height of the bow, when drawn, is 1.5 meters. Assume that prior to firing, the arrow is pulled back its entire length and is notched at the center of the bowstring. Assume also, albeit unrealistically, that the bow itself does not bend significantly. Calculate the speed of the arrow as it leaves the bow. You may also assume negligible gravitation.
The height of the wall is 7 meters. The lateral distance between Jin Ling and the monk is 24 meters. Calculate the amount of time Wei WuXian has to save Jin Ling’s life.
2. His Cultivator Senses™ tingling, Wei WuXian leaps heroically out of his hiding place at an angle of 30 degrees at a speed of 2 m/s. At the same time, he pulls out his flute and performs a beautiful overhand throw.
The trajectory of the arrow is perpendicular to the wall; Wei WuXian’s own trajectory is parallel to the wall. If Wei WuXian is 6 meters away from the wall and 8 meters away from the trajectory of the arrow, calculate the velocity at which HE will have to throw the flute to intercept the arrow.
A little-known fact about Wei WuXian: Any object he throws has a tendency to rotate about its center of mass at 5 radians per second. Fortunately, he is aware of this, and therefore you (the physics expert) are in charge of accounting for the spin. Lucky you. The flute is approximately 0.5 m and can be approximated as a rod of uniform density. The mass of the flute is about 0.2 kg. Calculate the work that Wei WuXian needs to perform on the flute to achieve the speed calculated in the previous section.
3. Success! The flute collides with the arrow and they stick together for a brief second before the flute breaks into a hundred tiny splinters.
Calculate the energy lost as heat in the collision.
Calculate the deflection of the arrow.