Final answer:
The solution to the question requires the use of projectile motion principles, specifically the time of flight in free fall and the formula d = v * t. However, the formula d(98) is unclear without further context or the full formula. The horizontal velocity v would normally be used to find the horizontal distance d if we knew the time the ball is in the air.
Step-by-step explanation:
To find the horizontal distance a ball travels after being rolled off a 30 meter cliff, we need to apply the principles of physics related to projectile motion. Unfortunately, the formula you mentioned in the question is missing. Normally, the horizontal distance (d) traveled by the projectile can be found using the formula d = v * t, where v is the horizontal velocity and t is the time the object is in the air. To calculate this, we would use the formula for the time of flight for an object in free fall from a height (h), which is t = sqrt(2h/g), where g is the acceleration due to gravity (9.8 m/s2). For a 30 meter cliff, this would give us t = sqrt(2*30/9.8)
However, since we need to calculate d(98), and we don't have a formula for d(v) expressed as a function of v, we cannot directly answer this question. Usually, we would calculate v if we knew the value of d at a certain time, but there seems to be an issue with the information provided.
For a similar problem, if a ball is rolled horizontally off a cliff and we know its horizontal velocity, we could calculate the horizontal distance traveled using the time it takes for the ball to fall to the ground based on its initial vertical velocity, which is zero in the case of being rolled horizontally.