Explanation:
This is true because at maximum height, the velocity is 0
State how much energy is transferred in each of the following cases: 2 grams of steam at 100 degrees Celsius condenses to water
1 answer:
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Answer: 288.8 m
Explanation:
We have the following data:
is the time it takes to the child to reach the bottom of the slope
is the initial velocity (the child started from rest)
is the angle of the slope
is the length of the slope
Now, the Force exerted on the sled along the ramp is:
(1)
Where is the mass of the sled and
its acceleration
In addition, if we draw a free body diagram of this sled, the force along the ramp will be:
(2)
Where is the acceleration due gravity
Then:
(3)
Finding :
(4)
(5)
(6)
Now, we will use the following kinematic equations to find :
(7)
(8)
Where is the final velocity
Finding from (7):
(9)
(10)
Substituting (10) in (8):
(11)
Finding :
(a)
Let's take the initial direction (before the collision) of the cue ball has positive x-direction.
Along the y-direction, the total initial momentum is zero:
Therefore, since the total momentum must be conserved, it must be zero also after the collision. So we write:
where
m is the mass of each ball
is the velocity of the cue ball after the collision
is the velocity of the second ball after the collision
is the angle of the cue ball with the x-axis
is the angle of the second ball
Solving for , we find the angle between the direction of motion of the second ball and the original direction of motion:
(b) 6.69 m/s
To find the original speed of the cue ball, we analyze the situation along the horizontal direction.
First, we calculate the total momentum along the x-direction after the collision, which is:
The initial total momentum along the x-direction as
where
m is the mass of the cue ball
is the initial velocity of the cue ball
The momentum along this direction must be conserved, so we can equate the two expressions and find the value of u: