- #1

VanessaN

- 12

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**Question 1)**An arrow with a mass of 80g is fired at an angle of 30 degrees to the horizontal. It strikes a target located 5 m above the firing point and impacts the target traveling at a speed of 20 meters/sec. If 10% of the initial energy of the arrow is lost to air resistance, what was the initial speed of the arrow?

**My attempt at the problem:**Energy final= Kf + Uf = 1/2*m*vf^2 + m*g*hf

Energy initial= Ki + Ui = 1/2*m*vi^2 + m*g*hi (but since initial height is 0)= 1/2*m*vi^2

Wnonconservative= Ei- Ef= 1/2*m*vi^2 -(1/2*m*vf^2 + m*g*hf)And since 10% of the initial energy is lost,

Wnonconservative= 0.1* Ei= 0.1* (1/2*m*vi^2)This next step is where I am getting confused, in solving for the initial speed:Wnonconservative= 1/2*m*vi^2 -(1/2*m*vf^2 + m*g*hf)so0.1* (1/2*m*vi^2)= 1/2*m*vi^2 -(1/2*m*vf^2 + m*g*hf)

The solution in the book is 23.5 m/s, but I don't know how to get it from here. Please help!

**Question 2)**Two different objects are dropped from rest off of a 50 m tall cliff. One lands going 30% faster than the other, and the two objects have the same mass. How much more kinetic energy does one object have at the landing than the other?

**My attempt at the problem:**

Vi=0

Vfinal, faster object= 1.3

Vfinal, slower object=1

initial height=50 m

final height= 0

mass,m

So the difference in kinetic energy is:

1/2 *m *(1.3v)^2 - 1/2 *m *v^2= ?

The answer is 69% more kinetic energy for the faster rock, but I'm having trouble finding out how to get that from here. Any help is very much appreciated! Thanks!