This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here is the solution: Given: Mass of bullet, m_b = 8.0 \, g = 0.008 \, kg Mass of wood cube, m_w = 9.00 \, kg Initial velocity of wood cube, u_w = 0 \, m/s (at rest) Final velocity of the combined bullet and wood cube, V = 40 \, cm/s = 0.40 \, m/s Initial velocity of bullet, u_b = ? Step 1: Apply the principle of conservation of momentum. Since the bullet lodges in the wood cube, this is an inelastic collision, and the total momentum before the collision equals the total momentum after the collision. m_b u_b + m_w u_w = (m_b + m_w)V Step 2: Substitute the known values into the equation. (0.008 \, kg)u_b + (9.00 \, kg)(0 \, m/s) = (0.008 \, kg + 9.00 \, kg)(0.40 \, m/s) (0.008)u_b + 0 = (9.008)(0.40) (0.008)u_b = 3.6032 Step 3: Solve for u_b. u_b = (3.6032)/(0.008) u_b = 450.4 \, m/s The initial velocity of the bullet is 450.4 m/s.