Final answer:
The initial speed of the bullet can be calculated using the equation v = √(vo^2 + 2ad), where vo is the initial speed, v is the final velocity, a is the acceleration, and d is the distance traveled. In this case, the initial speed of the bullet is zero.
Step-by-step explanation:
The initial speed of the bullet can be calculated using the equation v = √(vo^2 + 2ad), where vo is the initial speed, v is the final velocity, a is the acceleration, and d is the distance traveled. In this case, since the block is initially at rest on a frictionless table, the final velocity in the x direction is zero. So the equation becomes 0 = √(vo^2 + 2ad). Rearranging the equation, we can solve for vo:
vo = √(-2ad)
Since the bullet is traveling horizontally towards the east, there is no acceleration in the x direction. Therefore, a = 0. The distance traveled by the bullet can be calculated using the formula d = vt, where v is the initial velocity and t is the time. In this case, since the bullet strikes the block and stops, the time of travel is the same as the time it takes for the bullet to come to a stop. Thus, the distance traveled is zero. Substituting these values into the equation, we get:
vo = √(2 * 0 * 0)
Therefore, the initial speed of the bullet is zero.