A mass was dropped and pulled by Earth’s gravity. Acceleration due to gravity is
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Complete question:
The recoil of a shotgun can be significant. Suppose a 3.6-kg shotgun is held tightly by an arm and shoulder with a combined mass of 15.0 kg. When the gun fires a projectile with a mass of 0.040 kg and a speed of 380 m/s, what is the recoil velocity of the shotgun and arm–shoulder combination?
Answer:
The recoil velocity of the shotgun and arm–shoulder combination is 1.013 m/s
Explanation:
Given;
combined mass of the shotgun and arm–shoulder, m₁ = 15 kg
mass of the projectile, m₂ = 0.04 kg
speed of the projectile, u₂ = 380 m/s
let the recoil velocity of the shotgun and arm–shoulder combination = u₁
Apply the principle of conservation of linear momentum;
m₁u₁ + m₂u₂ = 0
m₁u₁ = - m₂u₂
Therefore, the recoil velocity of the shotgun and arm–shoulder combination is 1.013 m/s
The cart is moving by simple harmonic motion, and its position at time t is described by
where
A is the amplitude of the oscillation
is the angular frequency
The amplitude of the oscillation corresponds to the maximum displacement of the spring, which corresponds to the initial position where the spring was released:
A=0.250 m
The period of the motion is T=5.67 s, and the angular frequency is related to the period by
Therefore now we can calculate the position of the system at the time t=29.6 s:
where
A is the amplitude of the oscillation
The amplitude of the oscillation corresponds to the maximum displacement of the spring, which corresponds to the initial position where the spring was released:
A=0.250 m
The period of the motion is T=5.67 s, and the angular frequency is related to the period by
Therefore now we can calculate the position of the system at the time t=29.6 s: