Two planes of the same mass collide head-on and becomes tangled so that they move on together. If the engines of both were stopped at the moment of impact and the speeds of the planes at impact were 120m/s and 200 m/s, find the joint velocity immediately after collision.
Apply the conservation of momentum law, using the appropriate sign for velocity. If the 120 m/s plane (#1) is going in the + direction, the 200 m/s plane (#2) is going in the - direction.
Each plane has mass M.
Momentum conservation requires:
MV1 -MV2 = 2M*Vfinal
Vfinal = (1/2)(V1 - V2) = -40 m/s
thanx
To find the joint velocity immediately after the collision, we can use the principle of conservation of linear momentum.
The linear momentum of an object is given by the product of its mass and velocity. According to the conservation of linear momentum, the total linear momentum before the collision should be equal to the total linear momentum after the collision.
Let's denote the mass of each plane as m.
Before the collision:
The linear momentum of the first plane is given by P1 = m * v1, where v1 is the velocity of the first plane.
The linear momentum of the second plane is given by P2 = m * v2, where v2 is the velocity of the second plane.
The total linear momentum before the collision is P_total_before = P1 + P2 = m * v1 + m * v2.
After the collision:
The planes become tangled and move on together with a joint velocity, which we need to find. Let's call this joint velocity v_joint.
The linear momentum of the tangled planes after the collision is given by P_joint = 2m * v_joint, since the mass of the tangled planes is the sum of the masses of the individual planes.
According to the conservation of linear momentum, the total linear momentum after the collision should be equal to the total linear momentum before the collision:
P_total_before = P_joint.
Substituting the expressions for linear momentum before and after the collision, we have:
m * v1 + m * v2 = 2m * v_joint.
Now, we can solve for v_joint:
v_joint = (m * v1 + m * v2) / 2m.
Simplifying:
v_joint = (v1 + v2) / 2.
Substituting the given values:
v_joint = (120 m/s + 200 m/s) / 2.
v_joint = 320 m/s / 2.
v_joint = 160 m/s.
Therefore, the joint velocity immediately after the collision is 160 m/s.
To find the joint velocity immediately after the collision, we need to understand the concept of conservation of momentum. According to Newton's third law of motion, the total momentum before the collision is equal to the total momentum after the collision.
Momentum can be calculated by multiplying the mass of an object by its velocity. In this case, both planes have the same mass, so we can represent their masses as 'm'. The momentum of the first plane (plane A) before the collision is given by:
Momentum of plane A before collision = mass of plane A × velocity of plane A
= m × 120 m/s
Similarly, the momentum of the second plane (plane B) before the collision is given by:
Momentum of plane B before collision = mass of plane B × velocity of plane B
= m × 200 m/s
Since the planes become tangled and move on together after the collision, their total mass remains the same. Therefore, the total momentum after the collision is:
Total momentum after the collision = (mass of plane A + mass of plane B) × joint velocity
= (2m) × joint velocity
= 2mv
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can equate the two expressions:
m × 120 m/s + m × 200 m/s = 2mv
Simplifying the equation:
120 m + 200 m = 2v
320 m = 2v
Dividing both sides by 2:
v = 320 m / 2
v = 160 m/s
Hence, the joint velocity immediately after the collision is 160 m/s.