A 1 kg poodle running right at 3 m/s has an elastic head on collision with a 9 kg basset hound walking left with a velocity of 1 m/s. After the collision the poodle bounces off to the left at 3 m/s. Whats the basset hounds velocity after the colllision?
To solve this problem, we can apply the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is defined as the product of its mass and velocity. Mathematically, momentum (p) is given by the formula:
p = m * v
where p is momentum, m is mass, and v is velocity.
Let's calculate the momentum before the collision for both the poodle and the basset hound.
Momentum of the poodle before the collision:
mass of poodle (m1) = 1 kg
velocity of poodle (v1) = 3 m/s
p1 = m1 * v1
= 1 kg * 3 m/s
= 3 kg m/s (to the right)
Momentum of the basset hound before the collision:
mass of basset hound (m2) = 9 kg
velocity of basset hound (v2) = -1 m/s (since it is walking left)
p2 = m2 * v2
= 9 kg * (-1 m/s)
= -9 kg m/s (to the left) [note: negative sign indicates direction]
Now, let's consider the momentum after the collision. We know that the poodle bounces off to the left at 3 m/s. The basset hound's velocity after the collision is what we need to find.
Momentum of the poodle after the collision:
mass of poodle (m1) = 1 kg
velocity of poodle (v3) = -3 m/s (since it bounces off to the left)
p3 = m1 * v3
= 1 kg * (-3 m/s)
= -3 kg m/s (to the left)
According to the law of conservation of momentum, the total momentum before the collision must be equal to the total momentum after the collision.
Total momentum before = Total momentum after
(p1 + p2) = (p3 + p4)
Substituting in the known values:
(3 kg m/s - 9 kg m/s) = (-3 kg m/s + p4)
Simplifying the equation:
-6 kg m/s = p4
Therefore, the basset hound's momentum after the collision is -6 kg m/s (to the left).
To calculate the basset hound's velocity after the collision, divide its momentum by its mass:
velocity of basset hound after the collision (v4) = p4 / m2
= -6 kg m/s / 9 kg
= -0.67 m/s (approximately) [to the left]
Therefore, the basset hound's velocity after the collision is approximately -0.67 m/s (to the left).