Question

1.5 An airplane is flying at a given speed 'V' and at a given angle e above the horizontal. When the plane is 'h'meters above a spot on the level ground, a piece of luggage falls from the airplane. Determine the distance'x'between the spot on the ground and the location where the luggage lands. Place the options presented in the pull-down menu into the correct order to solve this problem. Not all options are valid steps in the solution. Not all options are needed for a solution. Note: Two of the options could be listed either second or third. Of the two, place the option that happens earlier chronologically in second place. Calculate the total time of flig v Calculate the total time of flight of the luggage Calculate the time it takes for the luggage to fall h meters to the ground on its way down. Calculate x from the plane's horizontal speed and the luggage's total time of flight. Calculate the maximum height the luggage reaches above the point where it left the airplane. Calculate the time it takes for the luggage to reach its maximum height. Calculate the horizontal and vertical components of the plane's velocity when the luggage fell from the plane Use the range equation to find the horizontal distance, x, the luggage travels until it strikes the ground. 2 3 4 Calculate the maximum heigh Calculate the time it takes for

Answer 1

When the luggage falls from the airplane it has same velocity as the velocity of airplane and after falling it starts moving like a freely falling body under gravity ie; motion will be a projectile motion in a given plane .

All calculation and work is shown below.

Given, Horizontal motion u_x = v cos e = initial vel. a_x = 0 = acceleration in x-direction v_x = Final velocity in x-direction v_x = v cos e Vertical motion u_y = v_y sin e a_y = -g v_y prime = u_y - gt = v_y sin e - gt. To calculate horizontal and vertical components of plane's velocity when luggage fell: Horizontal component, u_x = v cos e Vertical component: u_y = v sin e To calculate maximum height luggage reach: use equation H = u^2 sin^2 theta/2g substitute theta = e H = u^2 sin^2 (e)/2g Time of flight for projectile motion: T = 2u sin theta/g i.e t = 2u sin e/g So, v_y prime = v_y sin e - g (2v sin e/g) = v_y sin e - 2 v sin e. v_y prime = v sin e = -v sin e [negative sign shown -y direction] \r\n Time it takes for the luggage to fall h metres to the ground