Final answer:
The time it takes for a fruit to fall from a 20-meter tall tree to the ground can be calculated using the kinematic equation for free-fall, resulting in an approximate time of 2.02 seconds.
Step-by-step explanation:
To calculate the time it takes for a fruit to fall to the ground from a height of 20 meters, we can use the kinematic equation for free-fall motion under constant acceleration due to gravity. The equation is s = ut + 0.5at², where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time.
Since the fruit is dropping, its initial velocity u is 0 m/s, and the acceleration a due to gravity is approximately 9.81 m/s² downward. We are given the displacement s as -20 meters (negative since it falls downward).
Plugging these values into the equation:
-20 = (0)(t) + 0.5(9.81)t²
This simplifies to:
-20 = 4.905t²
Dividing both sides by -4.905 to solve for t²:
t² = 20/4.905
t² = 4.076 s²
Taking the square root of both sides gives us the time t = √4.076, which is approximately:
t ≈ 2.02 seconds (only the positive square root is considered because time cannot be negative).
The fruit takes approximately 2.02 seconds to reach the ground from the height of 20 meters.