Answer:
The shortest distance is 
Explanation:
The free body diagram of this question is shown on the first uploaded image
From the question we are told that
The speed of the bicycle is 
The distance between the axial is 
The mass center of the cyclist and the bicycle is 
behind the front axle
The mass center of the cyclist and the bicycle is 
above the ground
For the bicycle not to be thrown over the
Momentum about the back wheel must be zero so
=> 
=> 
Here 
So 
Apply the equation of motion to this motion we have
Where 
and 
since the bicycle is coming to a stop
=>
Answer:
The rise in height of combined block/bullet from its original position is 0.45m
Explanation:
Given;
mass of bullet, m₁ = 12 g = 0.012 kg
mass of block of wood, m₂ = 1 kg
initial speed of bullet, u₁ = 250 m/s.
initial speed of block of wood, u₂ = 0
From the principle of conservation of linear momentum, calculate the final speed of the combined block/bullet system.
m₁u₁ + m₂u₂ = v(m₁+m₂)
where;
v is the final speed of the combined block/bullet system.
0.012 x 250 + 0 = v (0.012 + 1)
3 = v (1.012)
v = 3/1.012
v = 2.96 m/s
From the principle of conservation of energy, calculate the rise in height of the block/bullet combined from its original position.
¹/₂mv² = mgh
¹/₂v² = gh
¹/₂ (2.96)² = (9.8)h
4.3808 = 9.8h
h = 4.3808/9.8
h = 0.45 m
Therefore, the rise in height of combined block/bullet from its original position is 0.45m
Answer:
The well is 23.3 m
Explanation:
As the bucket is lifted out of the well, energy in the man is being transferred to the bucket as gravitational potential energy.
Work done against gravity = mass * height * acceleration due to to gravity
W = mgh
5 920 J = 25.9 kg * h * 9.8 m/s²
h = 23.3 m
