Final answer:
To find the initial speed of the bullet fired into a ballistic pendulum, we can use the principle of conservation of momentum and conservation of energy. The initial speed can be calculated using the given mass of the bullet and bob, the height the bob rises, and the acceleration due to gravity.
Step-by-step explanation:
To determine the initial speed of the bullet, we can use the principle of conservation of momentum and conservation of energy. Since the bullet embeds in the pendulum bob, the total momentum before the collision is equal to the total momentum after the collision. We can write the equation:
bullet momentum = bob momentum
mv = (m+M)V
Where m is the mass of the bullet, M is the mass of the bob, and V is the velocity of the bullet and bob after the collision. Using this equation, we can solve for V:
V = (mv) / (m+M)
Once we know the velocity, we can use the conservation of energy to find the initial speed:
initial KE of bullet = KE of bullet and bob system
1/2 mv^2 = (m+M)gh
Where g is the acceleration due to gravity and h is the height the bob rises. Rearranging the equation, we can solve for the initial speed of the bullet:
Initial speed of the bullet = sqrt(2(m+M)gh)/m
Plugging in the given values, we can calculate the initial speed of the bullet.