IP A white-crowned sparrow flying horizontally with a speed of 1.70 m/s folds its wings and begins to drop in free fall
How far does the sparrow fall after traveling a horizontal distance of 0.400 m
To find the distance the sparrow falls after traveling a horizontal distance of 0.400 m, we can use the equations of motion. We need to determine the time it takes for the sparrow to fall and then calculate the vertical distance using the equation for free fall.
First, let's find the time it takes for the sparrow to fall. Since the horizontal distance remains constant during free fall, we can neglect any horizontal motion and focus on the vertical motion. In this case, the initial vertical velocity is 0 m/s since the sparrow is just starting to fall and the final vertical position is also 0 m (assuming the ground is at the same level as the starting point). The acceleration due to gravity, g, is approximately 9.8 m/s^2.
We can use the equation for vertical displacement in free fall:
Δy = v₀t + (1/2)gt²
Since the initial vertical velocity (v₀) is 0 m/s, the equation simplifies to:
Δy = (1/2)gt²
We need to find the time it takes to fall, so we rearrange the equation:
t = √(2Δy/g)
Substituting the known values:
t = √(2 * 0 / 9.8)
As the vertical displacement is zero (since the sparrow falls at the same height as it started), the time taken to fall is also zero.
Since the time is zero, the sparrow covers no vertical distance and falls vertically downwards.
Therefore, the sparrow falls a vertical distance of 0 meters after traveling a horizontal distance of 0.400 m.
well, it takes 0.4/1.7 = 0.235s to travel that distance.
now use your usual equation of motion to find the vertical distance fallen in that time.