Question

You drop a batitin a stationary elevator and the ball hits the floor in o 50 s. How long does it take for the ball to hit the floor if the elevator was atready moving up with a constant speed of 1 0 m's when you dropped the ball: Select one a. 0.61 s b. 0.82 s c. 0.41 s d. 0.50 s

Answer 1

Answer:

option (a) 0.61 s

Explanation:

Given;

Time taken by the ball to reach the ground  = 0.50 s

Let us first calculate the distance through which the ball falls on the ground

from the Newton's equation of motion, we have

$s=ut+\frac{1}{2}at^2$

where,  

s is the distance

a is the acceleration

t is the time

here it is the case of free fall

thus, a = g = acceleration due to gravity

u =  initial speed of the ball = 0

on substituting the values, we get

$s=0\times 0.50+\frac{1}{2}\times9.8\times0.50^2$

or

s = 1.225 m

Now,

when the elevator is moving up with speed of 1.0 m/s

the initial speed of the ball = -1.0 m/s   (as the elevator is moving in upward direction)

thus , we have

$s=ut+\frac{1}{2}at^2$

or

$1.225=-1.0\times\ t+\frac{1}{2}\times9.8t^2$

or

4.9t^2 - t  - 1.225 = 0

or

t = 0.612 s

hence, the correct answer is option (a) 0.61 s