Answer :
Final answer:
To determine the speed of the plane, we need to calculate the time the bag of sand is in the air due to gravity and use that time to calculate the horizontal distance traveled, which equals the plane's speed multiplied by the time.
Explanation:
The student's question is about determining the speed of the plane based on the time it takes for a bag of sand dropped from the plane to hit the ground. To solve for the speed, we must consider the vertical and horizontal components of the motion separately. The vertical component is dictated by the acceleration due to gravity, which allows us to determine how long it takes for the bag to hit the ground, while the horizontal component is the constant speed of the plane.
Since the bag hits the ground in 5 seconds and is dropped from an altitude of 800 meters, we can use the equation of motion s = ut + (1/2)at2 vertically, where u is the initial velocity (0 m/s vertically), a is the acceleration due to gravity (~9.81 m/s2), and t is the time (5 seconds). Solving for the horizontal distance traveled involves calculating the constant horizontal velocity of the plane. We know this distance must be the same as the point where the bag of sand hits the ground.