A 30g bullet with a speed of 400m=s strikes a glancing blow to a
target brick of mass 1:0kg. The Brick breaks into two fragments.
The bullet deflects at a angle of 30� above the +x-axis and has a
reduced speed of 100m=s. One piece of the brick with mass
(0.75kg) goes off to the right with a speed of 5:0m=s. Determine
the speed and direction of the other piece of the brick immediately
after the collison.
wat the hell ??
To determine the speed and direction of the other piece of the brick immediately after the collision, we can use the principle of conservation of momentum along the x-axis and y-axis. The momentum before the collision must be equal to the momentum after the collision.
First, let's find the initial momentum of the bullet and the brick before the collision.
Initial momentum of the bullet:
m_bullet = 30g = 0.03kg (convert from grams to kilograms)
v_bullet = 400 m/s
Initial momentum of the bullet along the x-axis (p_x_bullet_initial):
p_x_bullet_initial = m_bullet * v_bullet * cos(θ)
θ = 30 degrees
p_x_bullet_initial = 0.03kg * 400 m/s * cos(30 degrees)
Initial momentum of the bullet along the y-axis (p_y_bullet_initial):
p_y_bullet_initial = m_bullet * v_bullet * sin(θ)
p_y_bullet_initial = 0.03kg * 400 m/s * sin(30 degrees)
Next, let's find the initial momentum of the brick:
m_brick = 1.0kg
v_brick = 0 m/s (since it's initially at rest)
Initial momentum of the brick along the x-axis (p_x_brick_initial):
p_x_brick_initial = m_brick * v_brick
Initial momentum of the brick along the y-axis (p_y_brick_initial):
p_y_brick_initial = m_brick * v_brick
Now, let's find the final momentum of the bullet and the two pieces of the brick after the collision.
Final momentum of the bullet:
v_bullet_final = 100 m/s
θ_final = 30 degrees
Final momentum of the bullet along the x-axis (p_x_bullet_final):
p_x_bullet_final = m_bullet * v_bullet_final * cos(θ_final)
Final momentum of the bullet along the y-axis (p_y_bullet_final):
p_y_bullet_final = m_bullet * v_bullet_final * sin(θ_final)
Mass of one piece of the brick (m_brick_piece1):
m_brick_piece1 = 0.75kg
Velocity of one piece of the brick (v_brick_piece1):
v_brick_piece1 = 5.0 m/s (to the right)
Mass of the other piece of the brick (m_brick_piece2):
m_brick_piece2 = m_brick - m_brick_piece1
Velocity of the other piece of the brick (v_brick_piece2):
v_brick_piece2 = ? (to be determined)
Finally, let's apply the conservation of momentum equations:
Conservation of momentum along the x-axis:
p_x_bullet_initial + p_x_brick_initial = p_x_bullet_final + (m_brick_piece1 * v_brick_piece1) + (m_brick_piece2 * v_brick_piece2)
Conservation of momentum along the y-axis:
p_y_bullet_initial + p_y_brick_initial = p_y_bullet_final + (m_brick_piece1 * 0) + (m_brick_piece2 * 0)
By solving these two equations, you can find the value of v_brick_piece2, which will give you the speed and direction of the other piece of the brick immediately after the collision.