Zero Gravity

Classical Mechanics Level 2

A body is dropped from height $h$ meters. The gravitational field is nullified after the body travels half the distance. Concretely, when the body reaches $h/2$ , then $g \rightarrow 0$ . Find an expression for the time taken by the body to reach the ground.

If you get the answer as $\frac { a }{ b } \sqrt { \frac { h }{ g } }$ , where $a$ and $b$ are coprime integers, find ${ (a+b) }^{ 3 }-1$

Given that $a$ and $b$ are co prime natural numbers.

The answer is 124.

1 solution

Diamantis Koreas
Jul 19, 2015

For the first half of the distance we have: h/2 =1/2 g t^2. That gives time: t=sqrt(h/g) sec. For the second part we have g=0 and initial velocity v=g sqrt(h/g)=sqrt(g h). So we can find the time to cover the dropped body the last h/2 metres by the equation: h/2 =v * t = sqrt(g*h) * t. Solving it we get t=1/2 * sqrt(h/g) seconds. Adding the times for both parties we get a total time 3/2 *sqrt(h/g).

@diamantis koreas I would advice you to use LaTeX or the solution gets difficult to read. Also, You didn't calculate the final answer.

Mehul Arora - 5 years, 11 months ago

Thank you. You have right and I will use Latex next time. The calculation for the final answer is obvious: a= 3, b=2 and (a+b)^3 - 1 =(3+2)^3 - 1 =125-1= 124.

diamantis koreas - 5 years, 10 months ago

Haha, I know. Though You should add it for the clarity of your answer :)

Mehul Arora - 5 years, 10 months ago

@Swapnil Das Please check the reports.

Mehul Arora - 5 years, 11 months ago

Zero Gravity

The answer is 124.

1 solution

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