A bullet strikes a uniform plank with a speed of 400ms-¹ and comes out with the half the velocity . what would be the velocity if the plank were only half thick?
To find the final velocity of the bullet when the plank is only half as thick, we can use the principle of conservation of momentum. According to this principle, the momentum before the collision should be equal to the momentum after the collision.
Let's assume the initial velocity of the bullet is v1, and the final velocity is v2. We're given that v1 = 400 m/s and v2 = v1/2.
First, let's calculate the initial momentum of the bullet:
Initial momentum = mass × initial velocity
The mass of the bullet is not provided, but since we're only interested in the ratio of the velocities, we can ignore the mass. Therefore, the initial momentum is v1.
Next, let's calculate the final momentum of the bullet:
Final momentum = mass × final velocity
Again, since we're only interested in the ratio of the velocities, we can ignore the mass. Therefore, the final momentum is v2.
According to the conservation of momentum principle:
Initial momentum = Final momentum
v1 = v2
Substituting the given values:
400 m/s = (400 m/s) / 2
Now we can solve for v2:
v2 = (400 m/s) / 2
v2 = 200 m/s
So, the final velocity of the bullet when the plank is half as thick would be 200 m/s.