The Amazing Human Cannonball

Source: picgifs.com

The amazing human cannonball show is coming to town, and you are asked to double-check their calculations to make sure no one gets injured! The human cannonball is fired from a cannon that is a distance $x_1$ from a vertical wall with a hole through which the cannonball must fly. The lower edge of the hole is at height $h_1$ and the upper edge is at height $h_2$. The initial velocity of the cannonball is given as $v_0$ and you also know the angle $\theta $ of the cannon relative to the ground.

Thanks to their innovative suits, human cannonballs can fly without air resistance, and thus their trajectory can be modeled using the following formulas:

\begin{eqnarray*} x(t) & = & v_0 t \cos {\theta } \\ y(t) & = & v_0 t \sin {\theta } - \frac{1}{2} g t^2 \end{eqnarray*}where $x(t), y(t)$ provides the position of a cannon ball at time $t$ that is fired from point $(0, 0)$. $g$ is the acceleration due to gravity ($g = 9.81\ \text {m}/\text {s}^2$).

Write a program to determine if the human cannonball can make it safely through the hole in the wall. To pass safely, there has to be a vertical safety margin of $1$ m both below and above the point where the ball’s trajectory crosses the centerline of the wall.

The input will consist of up to $100$ test cases. The first line contains an integer $N$, denoting the number of test cases that follow. Each test case has $5$ parameters: $v_0 \ \theta \ x_1 \ h_1 \ h_2$, separated by spaces. $v_0$ ($0 < v_0 \le 200$) represents the ball’s initial velocity in m/s. $\theta $ is an angle given in degrees ($0 < \theta < 90$), $x_1$ ($0 < x_1 < 1000$) is the distance from the cannon to the wall, $h_1$ and $h_2$ ($0 < h_1 < h_2 < 1000$) are the heights of the lower and upper edges of the wall. All numbers are floating point numbers.

If the cannon ball can safely make it through the wall,
output “`Safe`”. Otherwise, output
“`Not Safe`”!

Sample Input 1 | Sample Output 1 |
---|---|

11 19 45 20 9 12 20 45 20 9 12 25 45 20 9 12 20 43 20 9 12 20 47.5 20 9 12 20 45 17 9 12 20 45 24 9 12 20 45 20 10 12 20 45 20 9 11 20 45 20 9.0 11.5 20 45 18.1 9 12 |
Not Safe Safe Not Safe Not Safe Not Safe Not Safe Not Safe Not Safe Not Safe Safe Safe |