To solve this problem, we need to consider the effects of gravity on the ball as it falls downward. The velocity of the ball changes over time due to the acceleration caused by gravity.
We can use the equations of motion to determine the velocity and distance of the ball after 8 seconds.
The equation for velocity is:
v = u + at
where: v = final velocity u = initial velocity a = acceleration t = time
In this case: u = 15 m/s (initial speed) a = acceleration due to gravity = 9.8 m/s² (assuming no air resistance) t = 8 s (time)
Plugging in the values, we can calculate the velocity after 8 seconds:
v = 15 m/s + (9.8 m/s²)(8 s) v = 15 m/s + 78.4 m/s v ≈ 93.4 m/s
Therefore, the velocity of the ball after 8 seconds is approximately 93.4 m/s downward.
To find the distance from the cliff to the drop point, we can use the equation for distance covered during uniform acceleration:
s = ut + (1/2)at²
where: s = distance u = initial velocity t = time a = acceleration
In this case: u = 15 m/s (initial speed) a = acceleration due to gravity = 9.8 m/s² (assuming no air resistance) t = 8 s (time)
Plugging in the values, we can calculate the distance covered:
s = (15 m/s)(8 s) + (1/2)(9.8 m/s²)(8 s)² s = 120 m + (1/2)(9.8 m/s²)(64 s²) s = 120 m + (1/2)(9.8 m/s²)(4096 s²) s = 120 m + 2008 m s = 2128 m
Therefore, the distance from the cliff to the drop point is approximately 2128 meters.