Question

two bodies of masses m1 and m2 are released from heights h1 and h2 respectively.obtain the ratio of time taken by both the bodies to reach to the earth​

Answer 1

Please refer to the attachment for the solution......

Hope u get that right.....

Answer 2

The ratio of time taken by both the bodies to reach the earth is $\frac{\text{t}_1}{\text{t}_2} = \sqrt{\frac{\text{h}_1}{\text{h}_2}}$

Explanation:

Given Data:

Two bodies were dropped ,with

$\text{Mass of the body X } = \text{m}_1$

$\text{Mass of the body Y } = \text{m}_2$

$\text{Height of the body X} = \text{h}_1$

$\text{Height of the body Y} = \text{h}_2$

Free Fall formula - The formula used for objects which are dropped from certain height.

                             $\text{h} = \frac{1}{2} \times \text{g} \times \text{t}^2$

Where 't' is the time taken by the object to reach the earth or ground.

Let us consider,

$\text{t}_1 \ \text{be the time taken by the body X}$

$\text{t}_2 \ \text{be the time taken by the body Y }$                      

For X, the free fall formula can be written as,

$\text{h}_1 = \frac{1}{2} \times \text{g} \times \text{t}_1^2 -----> (1)$

For Y, the free fall formula can be written as,

$\text{h}_2 = \frac{1}{2} \times \text{g} \times \text{t}_2^2 ----->(2)$

On dividing (1) and (2), we get

$\frac{\text{h}_1}{\text{t}_1^2} = \frac{\text{h}_2}{\text{t}_2^2}$

$\frac{\text{t}_1^2}{\text{t}_2^2} = \frac{\text{h}_1}{\text{h}_2}$

$\frac{\text{t}_1}{\text{t}_2} = \sqrt{\frac{\text{h}_1}{\text{h}_2}}$

The ratio of time taken both the bodies X and Y to reach the earth is  $\frac{\text{t}_1}{\text{t}_2} = \sqrt{\frac{\text{h}_1}{\text{h}_2}}$ .

To Learn More

1) Two bodies are thrown with the same initial velocity at angles theta and (90-theta) respectively with the horizontal,then their maximum heights are in ratio?

https://brainly.in/question/1600582

2) Two stones are thrown vertically upwards simultaneously with their initial velocities u1 and u2 respectively . Prove that the heights reached by them would be in the ratio of u1² :u2²

https://brainly.in/question/129691