Please help out college physics questions. PHYsics :(?

Question

1) A 19 g rifle bullet traveling 250 m/s buries itself in a 3.1 kg pendulum hanging on a 2.7 m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum's displacement.
vertical ______m 
horizontal____m

2) Two astronauts, one of mass 60 kg and the other 82 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 13 m?
______m

3) A ball of mass m makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to one-third its original speed. What is the mass of the second ball? (Use the following as necessary: m)
M2= _____

Ossi G · Accepted Answer

1) the initial velocity of the pendulum will be
v = m1v1/(m1+m2) = 0.019 kg*250 m/s/(3.119 kg) = 1.5229 m/s 

te kinetic energy is changed into potential energy
1/2 mv^2 = mgh 
v^2/2  =  gh
h = v^2/(2g) = 1.5229^2/(2*9.81) = 0.1182 m

the horizontal displacement is
x = √(2.7^2 - (2.7-0.1182)^2) = 0.7901 m

the final coordinates are (0.7901, 0.1182) 
------------
the velocity of 82 kg astronaut is v*60/82 = 0.7317v when v is the velocity of the lighter astronaut.
and when the lighter astronaut has moved 13 m, the distance moved by the heavier is
13*60/82 m = 9.512 m
----------
the final velocity of the first ball is
v1' = 2(m1v1/(m1+m2) - v1 where v1 is the initial velocity of ball 1, and m1 is its mass. 
- v1/3 = 2(m1v1/(m1 + x*m1)) - v1  cancel out m
- v1/3 = 2(v1/(1 + x)) - v1  divide by v1
- 1/3 = 2(1/(1+x)) - 1
 2/3 = 2(1/(1+x))
1/3 = 1/(1+x)
3 = (1 + x)
2 = x 

the second ball had twice the mass of the first ball = 2m


OG

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Please help out college physics questions. PHYsics :(?

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