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Answer :
The launch speed of the toy rocket is 22.1 m/s. The momentum of the toy rocket is 182.5 kg m/s. To calculate the launch speed of the toy rocket, we can use the conservation of energy principle.
Conservation of energy principle is given by,
Initial Kinetic Energy + Potential Energy
= Final Kinetic Energy + Potential Energy
Here,
Initial Kinetic Energy is zero because toy rocket was initially at rest.
Potential Energy = mgh where
m = mass of the object,
g = acceleration due to gravity, and
h = height
Final Kinetic Energy is zero because toy rocket comes to rest at the maximum height.
Therefore, mgh = 1/2 * mv²
Where m = 5 kg,
g = 9.8 m/s²,
h = 25 m
Launch speed of the toy rocket = v
= [tex]\sqrt{(2 * g * h)}[/tex]
= [tex]\sqrt{(2 * 9.8 * 25)}[/tex]
≈ 22.1 m/s
At height of 20m, momentum of the toy rocket can be calculated as:
P = mv
Where m = 5 kg (mass of toy rocket) and v is the velocity of the rocket.
Momentum of the toy rocket = P = mv
Where m = 5 kg,
and v = speed of the rocket at a height of 20 m.
v² = u² + 2gh
where u = initial speed of the rocket,
g = acceleration due to gravity, and
h = difference in height
Final speed of the rocket at 20 m height = v
= sqrt[tex]\sqrt{(u^{2} + 2gh) }[/tex]
= sqrt[tex]\sqrt{(22.1 m/s^{2} + 2*9.81* 20) }[/tex]
≈ 36.5 m/s
Momentum of the rocket = P
= mv
= (5 kg)(36.5 m/s)
= 182.5 kg m/s
Thus, the launch speed of the toy rocket is 22.1 m/s, and the momentum of the toy rocket at a height of 20 m is 182.5 kg m/s.
Learn more about conservation of energy here:
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