Final answer:
To find the range of the sphere launched from a ramp, calculate the time taken to reach the floor using the total height and solve for time. Then multiply the time taken by the initial velocity to get the range.
Step-by-step explanation:
To calculate the range of the sphere, we can first find the time it takes for the sphere to reach the floor. Since the ramp is 1.2 m above the floor, the total height the sphere falls is 1.2 + 0.5*9.81*t^2, where t is the time taken. Setting this equal to 1.2 and solving for t gives us the time taken to reach the floor. To find the range, we can then multiply this time by the initial velocity of the sphere. So the range of the sphere is given by: range = initial velocity * time taken.