Question

An airplane flies horizontally at a speed of 358 km/h and drops a crate that falls to the horizontal ground below. Neglect air resistance.

If the altitude of the plane was 548 m, then how far, horizontally in meters, did the crate move as it fell to the ground?

Answer 1

To calculate the distance the crate moves horizontally as it falls, we need to find the time it takes for the crate to fall. The time can be found using the equation s = ut + (1/2)at^2, where s is the vertical displacement, u is the initial vertical velocity, a is the acceleration due to gravity, and t is the time. Solving for t, we find t = 11.1 s.

Step-by-step explanation:

To find the horizontal distance the crate moves as it falls to the ground, we need to calculate the time it takes for the crate to fall. The time can be found by using the equation s = ut + (1/2)at^2, where s is the vertical displacement, u is the initial vertical velocity, a is the acceleration due to gravity, and t is the time. The vertical displacement is given as 548 m, the initial vertical velocity is 0 m/s, and the acceleration due to gravity is 9.8 m/s^2.

Using the equation, we can solve for t: 548 = 0 × t + (1/2) × 9.8 × t^2. Rearranging and solving the quadratic equation, we find t = 11.1 s.

The horizontal distance is given by the equation d = v × t, where d is the distance, v is the horizontal velocity, and t is the time. The horizontal velocity is given as 358 km/h, which can be converted to m/s by multiplying by 1000/3600. Substituting the values, we get d = (358 × 1000/3600) × 11.1 = 994.4 m.