Final answer:
The apple takes approximately 1.6 seconds to fall from a 12.5m high tree and travels at a speed of approximately 15.68 m/s when it reaches the ground, using the physics equations of motion with the acceleration due to gravity being 9.8 m/s².
Step-by-step explanation:
Calculating Time and Speed of a Falling Apple
When an apple is dropped from a 12.5m high tree, it is subject to the acceleration due to gravity, which is 9.8 m/s². To determine the time it takes for the apple to fall, we can use the equation of motion for uniformly accelerated motion:
s = ut + 0.5at²
Where s is the distance (12.5m), u is the initial velocity (0 m/s since the apple is dropped), a is the acceleration due to gravity, and t is the time in seconds. Plugging the values into the equation:
12.5 = 0 + 0.5 × 9.8 × t²
This simplifies to:
t² = 12.5 / 4.9
t = √(12.5 / 4.9)
Calculating the square root gives us the time approximately 1.6 seconds.
To find out how fast the apple is traveling when it reaches the ground, we can use the other equation of motion:
v = u + at
Where v is the final velocity. Since u is 0, this equation simplifies to:
v = 9.8 × t
Using the time found above, v = 9.8 × 1.6, which means the apple's speed upon impact is approximately 15.68 m/s.