Question

An airplane flies horizontally at a speed of 375 km/h and drops a crate that falls to the horizontal ground below. Neglect air resistance.

If the altitude of the plane was 510 m, then how far, horizontally in meters, did the crate move as it fell to the ground?

Answer 1

To compute the horizontal distance traveled by the crate, calculate the time of fall using the equation t = √(2h/g), convert the plane's speed from km/h to m/s, and multiply the speed by the time of fall.

Step-by-step explanation:

To determine how far horizontally the crate moved as it fell to the ground, we need to know the time it took for the crate to reach the ground. Since the crate was dropped from a plane flying horizontally at a constant speed and we are neglecting air resistance, we can treat the crate's horizontal and vertical motions separately. The crate's vertical motion is solely affected by gravity.

We can use the formula for the time of fall in vertical motion, which is derived from the kinematic equations: t = √(2h/g), where t is the time in seconds, h is the height in meters, and g is the acceleration due to gravity (≈9.81 m/s²). Plugging in the height of 510 meters, we get t ≈ √(2*510/9.81), which gives us the time it took for the crate to hit the ground.

Next, we convert the plane's horizontal speed from km/h to m/s by using the conversion factor 1 km/h = ⅖ m/s. The plane's speed is 375 km/h, which converts to 375 * ⅖ m/s. Now we can compute the horizontal distance by multiplying the plane's horizontal speed in m/s by the time of fall we calculated earlier.