a 4.00kg object traveling westward at 25.0m/s hits a 15.0kg object at rest. the 4.00kg object bounces eastward at 8.00m/s. what is the speed and direction of the 15.0kg object?
Let westward velocity be positive and eastward velocity be negative.
Use conservation of momentum.
4*25 = 4*(-8) + 15 V
Solve for V
V = 132/15 m/s
8.8
To solve this problem, we can use 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.
The momentum (p) of an object is given by the equation p = m * v, where m is the mass of the object and v is its velocity.
Let's calculate the initial and final momenta of the system:
Initial momentum:
The initial momentum of the 4.00kg object is given by p1 = m1 * v1, where m1 = 4.00kg (mass of the 4.00kg object) and v1 = 25.0m/s (velocity of the 4.00kg object). Therefore, p1 = 4.00kg * 25.0m/s = 100.0kg·m/s.
Since the 15.0kg object is at rest (v2 = 0), its initial momentum (p2) is 0 (p2 = m2 * v2 = 15.0kg * 0 = 0).
Total initial momentum (p_initial) = p1 + p2 = 100.0kg·m/s + 0 = 100.0kg·m/s.
Final momentum:
After the collision, the 4.00kg object bounces eastward at 8.00m/s. Therefore, its final momentum (p1') is given by p1' = m1 * v1' = 4.00kg * 8.00m/s = 32.0kg·m/s.
Now, let's assume the 15.0kg object moves with a velocity v2' after the collision. We need to determine its speed and direction.
According to the conservation of momentum, the total final momentum (p_final) should be equal to the initial momentum (p_initial).
Total final momentum (p_final) = p1' + p2'.
Since p1' = 32.0kg·m/s, we can write the equation as follows:
100.0kg·m/s = 32.0kg·m/s + p2'.
To isolate p2', we subtract 32.0kg·m/s from both sides:
100.0kg·m/s - 32.0kg·m/s = p2'.
68.0kg·m/s = p2'.
Now, we have the momentum of the 15.0kg object (p2'). We can determine its velocity (v2') by using the equation p2' = m2 * v2', where p2' = 68.0kg·m/s and m2 = 15.0kg.
Rearranging the equation, we get:
v2' = p2' / m2 = 68.0kg·m/s / 15.0kg = 4.53m/s.
Therefore, the speed of the 15.0kg object after the collision is 4.53m/s. Since it collided with the 4.00kg object from the west direction, it will also move in the east direction, opposite to the direction of the 4.00kg object.