Final answer:
The white-crowned sparrow falls approximately 0.8 meters after traveling a horizontal distance of 0.400 m, calculated using the equations of motion for an object in free fall and the given horizontal speed.
Step-by-step explanation:
The question is asking how far a white-crowned sparrow will fall, given it begins in horizontal flight and then folds its wings to drop in free fall. As the sparrow folds its wings, it will no longer experience the lift that kept it at a steady height and will begin to fall due to gravity. Assuming there is no air resistance, the only force acting on the sparrow is the force of gravity.
To solve this, we can use the equations of motion for an object in free fall. The horizontal and vertical motions can be considered separately since they are independent. Given the horizontal velocity is 1.40 m/s and the horizontal distance traveled is 0.400 m, we can calculate the time it takes to cover that distance:
time = distance / horizontal speed = 0.400 m / 1.40 m/s = approximately 0.286 seconds.
Next, we use the time to find the vertical displacement using the formula for the distance traveled under constant acceleration, which for free fall is the acceleration due to gravity (approximately 9.81 m/s2):
distance fallen = 0.5 × gravity × time2 = 0.5 × 9.81 m/s2 × (0.286 s)2 ≈ 0.8 meters.
Thus, the sparrow falls approximately 0.8 meters after traveling a horizontal distance of 0.400 m.