A typical stellar spectrum (a plot of intensity versus wavelength) includes a number of deep indentations in which the intensity
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The initial potential energy of the wagon containing gold boxes will enable
it roll down the hill when cut loose.
The Lone Ranger and Tonto have approximately <u>5.1 seconds</u>.
Reasons:
Mass wagon and gold = 166 kg
Location of the wagon = 77 meters up the hill
Slope of the hill = 8°
Location of the rangers = 41 meters from the canyon
Mass of Lone Ranger, m₁ = 65 kg
Mass of Tonto m₂ = 66 kg
Solution;
Height of the wagon above the level ground, h = 77 m × sin(8°) ≈ 10.72 m
Potential energy = m·g·h
Where;
g = Acceleration due to gravity ≈ 9.81 m/s²
Potential energy of wagon, P.E. ≈ 166 × 9.81 × 10.72 = 17457.0912
Potential energy of wagon, P.E. ≈ 17457.0912 J
By energy conservation, P.E. = K.E.
Where;
v = The velocity of the wagon a the bottom of the cliff
Therefore;
Velocity of the wagon, v ≈ 14.5 m/s
Momentum = Mass, m × Velocity, v
Initial momentum of wagon = m·v
Final momentum of wagon and ranger = (m + m₁ + m₂)·v'
By conservation of momentum, we have;
m·v = (m + m₁ + m₂)·v'
Which gives;
The velocity of the wagon after the Ranger and Tonto drop in, v' ≈ 8.1 m/s
The Lone Range and Tonto have approximately <u>5.1 seconds</u> to grab the
gold and jump out of the wagon before the wagon heads over the cliff.
Learn more here:
Force is defined as the rate of change of momentum.
The initial amount of momentum is
because water stops when it hit the wall total change of momentum must be 
.
Now let's calculate the force.
We need to find
. This is the amount of water hiting the wall per second.
Our final formula would be:
And now we can calculate the answer:
The initial amount of momentum is
Now let's calculate the force.
We need to find
Our final formula would be:
And now we can calculate the answer:
Answer:
The object will travel at the speed of 16 m/s.
Explanation:
Given
- Mass m = 4.0 kg
- Momentum p = 64 kgm/s
To determine
How fast is the object traveling?
<u>Important Tip:</u>
The product of the mass and velocity of an object — momentum.
Using the formula
where
- m = mass
- v = velcity
- p = momentum
Thus, in order to determine the speed of the object, all we need to do is to substitute p = 64 and m = 4 in the formula
switch the equation
divide both sides by 4
simplify
m/s
Therefore, the object will travel at the speed of 16 m/s.