To determine how long it will take for the second ball to overtake the first, we need to analyze the motion of both balls and find the time at which their positions are equal.
Let's consider the motion of the first ball, which is dropped off the cliff. Since it is dropped, its initial velocity is 0 m/s. The distance traveled by an object in free fall can be calculated using the equation:
d1 = (1/2) * g * t^2
Where: d1 is the distance traveled by the first ball, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time elapsed.
Given that 2 seconds have passed since the first ball was dropped, we can calculate the distance traveled by the first ball as:
d1 = (1/2) * 9.8 * (2)^2 = 19.6 m
Now, let's consider the motion of the second ball, which is thrown vertically downwards with an initial speed of 30 m/s. The equation for the distance traveled by an object with constant velocity can be used:
d2 = v * t
Where: d2 is the distance traveled by the second ball, v is the initial velocity of the second ball, and t is the time elapsed.
We want to find the time at which the positions of the two balls are equal, so we set d1 equal to d2:
19.6 = 30 * t
Solving this equation for t, we get:
t = 19.6 / 30 ≈ 0.653 seconds
Therefore, it will take approximately 0.653 seconds for the second ball to overtake the first.