In the Hunger Games, Katniss shoots an arrow at an apple in a pig’s mouth using a longbow. After careful analysis of the scene, my daughter and I estimate she is standing 12 m away and 3.5 m below her target. A typical shot from a longbow reaches speeds of 55 m/s.
a) At what angle above the horizontal must she fire the arrow? There are two solutions (what do they correspond to?) and which one would be the one she used (she wanted a sudden dramatic impact). Treat the arrow as a simple projectile.
b) How fast is arrow moving when it hits the apple?
c) After hitting the apple the arrow takes the apple with it and hits the wall half a meter behind the pig, how fast are the arrow and apple moving as they hit the wall? (A typical arrow has a mass of 18 grams, and a typical apple has a mass of 100 grams).
d) Suppose we model the bowstring as an ideal spring with spring constant k= 70 N/m, how far must Katniss draw the bow to give it the arrow an initial velocity of 55 m/s?
(A) x= horizontal distance of apple
y= vertical distance of apple
using y= x tan - gx^{2}/2u^{2}cos^{2}
3.5 = 12 tan - 10×12×12/2(55×55)(cos^{2})
3.5 = 12 tan - 0.238sec^{2}
3.5 = 12 tan - 0.238( 1 + tan^{2})
0.238 tan^{2} - 12 tan + 3.738=0
tan= (-(-12)+-(12^{2}-4×0.238×3.738)^{0.5})/(2×0.238)
= 17.40^{0} or 72.60^{0} with horizontal
She would shoot the arrow at 17.40 degree with horizontal for sudden impact.
(B) let speed of arrow on hitting apple =V
V=( (u cos)^{2} + ( u sin - gt)^{2})^{1/2}
Where t= time taken to hit apple
t= x/u cos = 12/ 55 cos(17.40)= 0.23 sec
V= ((55 cos(17.40))^{2} +(55 sin 17.40 - 10×0.23)^{2})^{1/2}
V= 54.36 m/s
(D) gain in kinetic energy by arrow = loss in potential energy of spring, let L = length drawn by arrow
(0.5 mu^{2}) = (0.5 kL^{2})
L= (mu^{2}/k)^{1/2}= ( 0.018×55×55/70)^{1/2} = 0.881 m
L= 88.1 cm
In the Hunger Games, Katniss shoots an arrow at an apple in a pig’s mouth using...
To receive full credit you must clearly show all DT YOU" of the proper use of units): I need enough information to be able to follow your understuu physics principles involved in each question or problem. Write your work on other sheets of paper and attach them to this page. 2 Had tam or w world Home Exercise #7 o 220m to na nga T (5) 1. Problem #30 from Chapter 9 2. Problem #44 from Chapter 9 totoolsvart notarib...