DMOPC '14 Contest 7 P1 - Flare - DMOJ: Modern Online Judge

DMOPC '14 Contest 7 P1 - Flare

Points: 3 (partial)

Time limit: 2.0s

Memory limit: 64M

Author:

Problem type

Stranded on an island, Tusk decides to launch a signalling flare, but forgets to angle it towards the water. As a result, it takes off perpendicular to the ground. Its height $y$ ~y~ in relation to its initial velocity $v$ ~v~, Earth's gravitation $g=-9.8\dfrac{m}{s^2}$ ~g=-9.8\dfrac{m}{s^2}~ and time $t$ ~t~ given as:

$\displaystyle y = vt + \frac{1}{2}gt^2$

If Ange launches the flare from the ground where $y=0$ ~y=0~ at time $t=0$ ~t=0~, how long does Ange have to get out of the way before the flare comes burning down?

Input Specification

A single integer, $v$ ~v~ $(1 \le v \le 10^9)$ ~(1 \le v \le 10^9)~.

Output Specification

The time elapsed until the flare touches the ground, i.e. the value of $t > 0$ ~t > 0~ such that the expression evaluates to $0$ ~0~. Your answer will be considered correct if it is within an absolute or relative error of $10^{-6}$ ~10^{-6}~.

Sample Input

Sample Output

2.040816

Explanation of Output for Sample Input

Substituting in $2.040816$ ~2.040816~ for $t$ ~t~, we find that $10 \times 2.040816 + \dfrac{1}{2} \times (-9.8) \times (2.040816)^2 \approx 0$ .

Here is a displacement-time graph of the flare:

$\text{[math]}$

Comments

0

sas5580 commented on May 5, 2015, 8:07 p.m.

First paragraph says Tusk, second says Ange

1

FatalEagle commented on May 5, 2015, 8:29 p.m.

Ange launches the flare Tusk prepared.

-9

omaewamoushindeiru commented on May 6, 2015, 3:39 a.m.

rip sas5580

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