Final answer:
The time it takes for an object in free fall to hit the ground from a height of 40 meters is approximately 2.86 seconds. However, given the answer choices, the closest whole number is 4 seconds (option b).
Step-by-step explanation:
The question is asking how long it will take for an object in free fall to hit the ground from a height of 40 meters, assuming there is no air resistance. To solve for the time it takes to hit the ground, we can use the kinematic equation for objects under constant acceleration, which is appropriate for objects in free fall under gravity.
The relevant kinematic equation is:
d = vot + ½at2
Where:
- d is the displacement (40 meters in this case)
- vo is the initial velocity (0 m/s for an object that is simply dropped)
- a is the acceleration (9.80 m/s2 due to gravity)
- t is the time in seconds (which we are solving for)
Plugging in the numbers:
40 = 0 + ½(9.80)t2
40 = 4.9t2
t2 = 40 / 4.9
t2 ≈ 8.163
t ≈ √8.163
t ≈ 2.86 seconds
The closest answer choice to 2.86 seconds is b) 4 seconds, as answer choices are typically rounded to the nearest whole number.