Question

if the altitude of the plane was 691 m, then how far, horizontally in meters, did the crate move as it fell to the ground?

Answer 1

The crate would move approximately 1643.92 meters horizontally as it fell to the ground, which is calculated by finding the time it takes for the crate to fall and then multiplying the horizontal velocity of the plane by the time of the crate's descent.

Step-by-step explanation:

To determine how far horizontally the crate moved as it fell to the ground, we need to calculate the time it takes for the crate to hit the ground and then use this time to figure out how far the plane would travel horizontally during the crate's descent. First, we can calculate the time of free fall using the formula for the free fall of objects under the acceleration due to gravity (assuming no air resistance) which is t = sqrt(2h/g), where h is the height or altitude, and g is the acceleration due to gravity (9.8 m/s2). Once we have the time (t), we can calculate the horizontal distance using the horizontal velocity of the plane and the formula distance = velocity x time. In this case, the actual altitude is 691 m and the horizontal velocity of the plane needs to be consistent with that used in the example, 500 km/h, which we convert into meters per second (m/s).

To solve the problem, we can proceed as follows:

1. Convert the plane's velocity from km/h to m/s: (500 km/h * 1000 m/km) / (3600 s/h) = 138.89 m/s.
2. Calculate the time of fall: t = sqrt(2 * 691 m / 9.8 m/s2) approx. 11.83 s.
3. Calculate the horizontal distance: distance = 138.89 m/s * 11.83 s = 1643.92 m.

Therefore, the crate would move approximately 1643.92 meters horizontally as it fell to the ground.