Answer :
Just before the explosion, the rocket has a velocity of 20.00 m/s. After the explosion, the heavier piece attains a speed of approximately 25.17 m/s.
The acceleration of the rocket is given as 5.00 m/s², and the time it takes for the explosion to occur is 4.00 s. To find the speed of the heavier piece just after the explosion, we can use the concept of acceleration and the equation of motion.
First, let's calculate the velocity of the rocket just before the explosion using the equation v = u + at, where v is the final velocity, u is the initial velocity (which is 0 m/s as the rocket starts from rest), a is the acceleration, and t is the time. Plugging in the values, we get:
v = 0 + (5.00 m/s²)(4.00 s)
v = 20.00 m/s
So the velocity of the rocket just before the explosion is 20.00 m/s.
After the explosion, the lighter piece continues to rise to a maximum height of 187 m. To find the velocity of the heavier piece just after the explosion, we can use the conservation of momentum.
The principle of momentum conservation states that the total momentum before the explosion is conserved and equal to the total momentum after the explosion. The momentum of an object can be calculated using the formula p = mv, where p represents the momentum, m denotes the mass of the object, and v represents its velocity. Let's denote the velocity of the heavier piece as v₁ and the velocity of the lighter piece as v₂.
Before the explosion: (88.1 kg)(20.00 m/s) = (70.0 kg)(v₁) + (m₂)(v₂)
Since the lighter piece reaches a maximum height of 187 m, we know that its final velocity is 0 m/s (at the highest point of the trajectory). Therefore, v₂ = 0.
Simplifying the equation, we have: (88.1 kg)(20.00 m/s) = (70.0 kg)(v₁)
Now we can solve for v₁: v₁ = (88.1 kg)(20.00 m/s) / (70.0 kg)
Calculating the value, we get: v₁ = 25.17 m/s
Therefore, the speed of the heavier piece of the toy rocket just after the explosion is approximately 25.17 m/s.
In summary, the velocity of the rocket just before the explosion is 20.00 m/s. The speed of the heavier piece just after the explosion is approximately 25.17 m/s.
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