Ihave three questions. john has to hit a bottle with a ball to win a prize. he throws a 0.4 kg ball with a velocity of 18 m/s. it hits a 0.2 kg bottle, and the bottle flies forward at 25 m/s. how fast is the ball traveling after hitting the bottle?
2. someone fires a 0.04 kg bullet at a block of wood that has a mass of 0.5 kg. (the block of woof is sitting on a frictionless surface, so it moves freely when the bullet hits it). the wood block is initially at rest. the bullet is traveling 300 m/s when it hits the wood block and sticks inside it. now the bullet and the woof block move together as one object. how fast are they traveling?
3. a big league hitter attacks a fastball. the ball has a mass of 0.16 kg. it is pitched at 38 m/s. after the player hits the ball, it is now traveling 44 m/s in the opposite direction. the impact lasted 0.002 seconds. how big of a force did the ballplayer put on that ball?

1. 5.5 m/s

We can solve the problem by applying the law of conservation of momentum. The total momentum before the collision must be equal to the total momentum after the collision, so we have:

where

m1 = 0.4 kg is the mass of the ball

u1 = 18 m/s is the initial velocity of the ball

m2 = 0.2 kg is the mass of the bottle

u2 = 0 is the initial velocity of the bottle (which is initially at rest)

v1 = ? is the final velocity of the ball

v2 = 25 m/s is the final velocity of the bottle

Substituting and re-arranging the equation, we can find the final velocity of the ball:

2. 22.2 m/s

We can solve the problem again by using the law of conservation of momentum; the only difference in this case is that the bullet and the block, after the collision, travel together at the same speed v. So we can write:

where

m1 = 0.04 kg is the mass of the bullet

u1 = 300 m/s is the initial velocity of the bullet

m2 = 0.5 kg is the mass of the block

u2 = 0 is the initial velocity of the block (which is initially at rest)

v = ? is the final velocity of the bullet+block, which stick and travel together

Substituting and re-arranging the equation, we can find the final velocity of bullet+block:

3. 6560 N

The impulse exerted on the ball is equal to its change in momentum:

(1)

The impulse can be rewritten as product between force and time of collision:

while the change in momentum of the ball is equal to the product between its mass and the change in velocity:

So, eq.(1) becomes

where:

F = ? is the unknown force

is the duration of the impact

m = 0.16 kg is the mass of the ball

is the final velocity of the ball

is its initial velocity (we must add a negative sign, since it is in opposite direction to the final velocity)

So, by using the equation, we can find the force:

-first use of geothermal energy occurred more than 10,000 years ago in north america by american paleo-indians

-the first industrial use of geothermal energy began near pisa, italy in late 18th century

-in 1904, italian scientist piero ginori conti invented the first geothermal electric power plant in which steam was used to generate the power

-with the above experiment, the first geothermal plant in usa started in 1922 with a capacity of 250 kilowatts

-however, in 1946 first ground-source geothermal heat pump installed at commonwealth building in portland, oregon

-during the 1960’s, pacific gas and electric began operation of first large scale geothermal power plant in san francisco, producing 11 megawatts

-in 1973, when oil crisis began many countries began looking for renewable energy sources and by 1980’s geothermal heat pumps (ghp) started gaining popularity in order to reduce heating and cooling costs

-as effect of climate change started showing results, governments of various countries joined hands to fight against it, for which kyoto protocol was signed in japan in 1997, laid out emission targets for rich countries and required that they transfer funds and technology to developing countries, 184 countries have ratified it

hope this