Final answer:
The problem involves calculating the initial velocity needed for a pebble to reach a certain height and distance in projectile motion. Missing data such as gravity's value makes it impossible to solve without making assumptions.
Step-by-step explanation:
The problem of Romeo throwing pebbles up to Juliet's window is a classic physics problem involving projectile motion. To ensure the pebbles hit the window with only a horizontal component of velocity, Romeo must throw the pebbles at a specific initial velocity that considers both the vertical distance (height) and the horizontal distance (range) to the window.
From the given information, Juliet's window is 8.0 m above Romeo's position, and the horizontal distance from Romeo to the base of the wall is 8.5 m. Using the equations of projectile motion, we can understand that the pebbles need to be thrown with an initial vertical velocity that will allow them to reach a height of 8.0 m. Since the problem asks for the pebbles to have only a horizontal component of velocity when they hit the window, this means they must reach the peak of their trajectory exactly at the height of the window. At the peak of their trajectory, vertical velocity is zero.
The time taken to reach this height can be calculated using the equation of motion under constant acceleration due to gravity. Once the time is known, we can calculate the initial horizontal velocity required to cover the horizontal distance in this same amount of time. However, the student did not provide enough information to solve this question, such as the effect of gravity or the potential need for an angle of throw, to complete the calculations required to determine the exact velocity.