A train slows down with constant deceleration a If a child d

A train slows down with constant deceleration a. If a child drops an apple in the dining car, what path does he observe the apple take? (Derive an expression for the apple\'s trajectory, y = f(x), and identify it.) If the inital height of the apple is y_0, find how far it is away from the child\'s feet when it hits the floor.

Solution

Horizontal force on apple = -ma

vertical force on apple= mg

x=ut+1/2at^2

for horizontal

x= -1/2at^2

y=-1/2 gt^2 if we take upward as postivie

now equating both we get y=(g/a)*x

b)time taken by apple to reach floor = (2*Y0/g)^1/2

horizontal distance covered in this time = 1/2 * a* t^2 = 1/2 *a*2y0/g =aY0/g