To determine the height the block will rise into the air, we can use the principle of conservation of momentum. The bullet's initial momentum is equal to the final momentum of the block and bullet combined. By solving the equations and using the formula for height of a projectile, we find that the block will rise 0.09 m into the air.
To determine the height the block will rise into the air, we can use the principle of conservation of momentum. Since the bullet becomes embedded in the block, the initial momentum of the bullet is equal to the final momentum of the block and bullet combined.
The momentum of an object is given by the product of its mass and velocity. Let's denote the initial velocity of the bullet as v and the final velocity of the block and bullet combination as V. We can then set up the following equation:
(mass of bullet)(initial velocity of bullet) = (mass of block + bullet)(final velocity of block and bullet)
Plugging in the given values, we have:
(0.024 kg)(310 m/s) = (1.5 kg + 0.024 kg)(V)
By solving this equation for V, we can find the final velocity of the block and bullet combination. Since the block started at rest, the final velocity is the velocity at which the block rises into the air. We can then use the formula for height of a projectile to find the height:
Height = (final velocity)^2 / (2 * acceleration due to gravity)
By plugging in the value for the final velocity and the standard value for acceleration due to gravity, we can calculate the height. The correct answer is option a) 0.09 m.