A 3.5 g dart is fired into a block of wood with a mass of 22.8 g. The wood block is initially at rest on a 1.3 m tall post. After the collision, the wood block and dart land 2.6 m from the base of the post. Find the initial speed of the dart.
m/s
To find the initial speed of the dart, we can use the principle of conservation of linear momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. So, we can write the momentum equation as:
(mass of dart) × (initial velocity of dart) = (mass of wood block) × (final velocity of wood block) + (mass of dart) × (final velocity of dart)
Given:
Mass of dart (m1) = 3.5 g = 0.0035 kg
Mass of wood block (m2) = 22.8 g = 0.0228 kg
Initial velocity of wood block (v2) = 0 m/s (since the block is initially at rest)
Final velocity of wood block (v2') = ?
Final velocity of dart (v1') = 0 m/s (since the dart comes to rest after the collision)
Now, let's calculate the final velocity of the wood block (v2'):
0.0035 kg × (initial velocity of dart) = 0.0228 kg × 0 m/s + 0.0035 kg × 0 m/s
0.0035 kg × (initial velocity of dart) = 0
Since the mass of the dart is non-zero, we can divide both sides of the equation by the mass of the dart:
(initial velocity of dart) = 0 / 0.0035 kg
We can't divide by zero, which means the initial velocity of the dart is indeterminate based on the information given.
Therefore, without additional information, we cannot determine the initial speed of the dart in this scenario.