An eagle (m1 = 5.2 kg) moving with speed v1 = 6 m/s collides with a second eagle (m2 = 4.8 kg) moving with speed v2 = 5.6 m/s in a direction at right angle to the first one. After the collision, they hold onto one another. With what speed are they moving after the collision
To find the speed at which the two eagles are moving after the collision, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Momentum is defined as the product of an object's mass and velocity. Mathematically, it can be expressed as:
Momentum = mass × velocity
Let's denote the speed at which the eagles move after the collision as v'. We can set up equations for the conservation of momentum in the x and y directions separately.
In the x direction:
Before the collision: m1 × v1 + m2 × v2 = momentum1
After the collision: (m1 + m2) × v' = momentum2
Since the collision occurs at a right angle, the momentum in the y direction before and after the collision is zero.
Let's plug in the given values into the equations:
m1 = 5.2 kg
v1 = 6 m/s
m2 = 4.8 kg
v2 = 5.6 m/s
Equation for the x direction:
5.2 kg × 6 m/s + 4.8 kg × 5.6 m/s = (5.2 kg + 4.8 kg) × v'
Now, we can solve for v':
47.2 kg·m/s = 10 kg × v'
47.2 kg·m/s = 10 kg × v'
v' = 47.2 kg·m/s / 10 kg
v' = 4.72 m/s
Therefore, after the collision, the two eagles are moving at a speed of 4.72 m/s.