Final answer:
To calculate the initial roll velocity of the bowling ball, apply the projectile motion equations to find the time it takes to fall 10 meters and use that time to calculate the horizontal velocity needed to cover the 9-meter distance.
Step-by-step explanation:
To determine with what velocity one should roll the bowling ball off the roof so that it hits the target, we need to consider the motion of the bowling ball as a problem of projectile motion without air resistance. The building is 10 meters tall, and the target is placed 9 meters away from the building horizontally.
Firstly, we need to calculate how long it will take for the ball to fall 10 meters. Without air resistance, the time 't' it takes for an object to fall can be found using the equation:
distance = 1/2 × gravity × time^2
For 10 meters and using g = 9.8 m/s² (acceleration due to gravity), we have:
10 = 1/2 × 9.8 × t^2
Solving for 't', we find:
t = sqrt(2 × 10 / 9.8)
Now, since we only need the horizontal component to determine initial roll velocity, we use the horizontal distance and time:
horizontal velocity = distance / time
horizontal velocity = 9 m / t
By substituting the time 't' solved previously, we can find the initial roll velocity required to hit the target.