what is the physics answer to A 25.0 kg mortar shell is launched from level ground at 38.0m/s at 60 Degrees above the horizontal. At the top of its trajectory, the shell explodes into three pieces. A 10.0 kg piece flies forward at 38.0 m/s. Another 10.0 kg piece flies straight up at 15.0m/s. What is the velocity of the remaining piece?
To find the velocity of the remaining piece, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event.
In this case, we can consider the explosion of the mortar shell as the event. Before the explosion, the entire mortar shell has momentum, and after the explosion, the three pieces have individual momenta. The sum of these individual momenta should be equal to the initial momentum of the mortar shell.
Given:
Mass of the mortar shell (m1) = 25.0 kg
Initial velocity of the mortar shell (v1) = 38.0 m/s
Mass of one piece (m2) = 10.0 kg (the piece flying forward)
Velocity of one piece (v2) = 38.0 m/s (same as the initial velocity)
Mass of another piece (m3) = 10.0 kg (the piece flying straight up)
Velocity of the other piece (v3) = 15.0 m/s
The initial momentum of the mortar shell is calculated by multiplying its mass with its initial velocity:
Initial momentum (p1) = m1 * v1
The momentum after the explosion is the sum of the individual momenta of the three pieces:
Final momentum (p2) = momentum of piece 2 + momentum of piece 3 + momentum of the remaining piece
The momentum of each piece can be calculated by multiplying the mass of the piece with its velocity:
Momentum of piece 2 (p2_2) = m2 * v2
Momentum of piece 3 (p2_3) = m3 * v3
Using the conservation of momentum, we can equate the initial momentum to the final momentum:
Initial momentum = Final momentum
m1 * v1 = p2_2 + p2_3 + momentum of the remaining piece
To find the velocity of the remaining piece, we need to rearrange the equation and solve for it. The equation becomes:
momentum of the remaining piece = (m1 * v1) - (p2_2 + p2_3)
Now we substitute the given values:
momentum of the remaining piece = (25.0 kg * 38.0 m/s) - (10.0 kg * 38.0 m/s + 10.0 kg * 15.0 m/s)
Calculate the momenta:
momentum of the remaining piece = (950 kg*m/s) - (380 kg*m/s + 150 kg*m/s)
Finally, calculate the momentum of the remaining piece:
momentum of the remaining piece = 950 kg*m/s - 530 kg*m/s = 420 kg*m/s
The velocity of the remaining piece can be found by dividing its momentum by its mass:
Velocity of the remaining piece = momentum of the remaining piece / mass of the remaining piece
Since we haven't been given the mass of the remaining piece, we can't directly find its exact velocity.