Problem F
Staying Onsides
It’s the $2018$
Champions League final, the pinnacle of European club soccer,
and the two finalist teams are at war for the tournament cup.
Real Madrid is coming in hot with a counter-attack for a goal
opportunity. Marcelo is about to cross the ball to Gareth Bale,
who is sprinting alongside the opponent’s defender, trying to
get in position to receive the pass. Bale, however, needs to be
careful with not being offsides. Once Marcelo kicks the ball
for the pass, Bale can not be ahead of the defender, though
being exactly beside the defender makes him safe.
We know the number of seconds before Marcelo passes the ball,
$s$, and we can also tell
the position $pd$ of the
defender and $pb$ of Bale,
both in meters away from the end line. On top of that, we also
have the defender’s constant speed $sd$ and Bale’s constant speed
$sb$, both in
meters/second. However, though the defender is running straight
towards the goal in a $90^{\circ
}$ angle from the right sideline, Bale is coming in at
an angle from the right sideline, $a$. Will Bale be offsides?
Input
The first line contains the integer $N$, the number of scenarios/test
cases given, where ($1 \leq N
\leq 10$).
Each test case is composed of three lines.
The first test case line contains two space-separated integers,
$s$, the number of
seconds, where ($1 \leq s \leq
5$), and $a$, the
angle of Bale’s run, where ($45
\leq a \leq 135$).
The second test case line contains two space-separated integers
denoting the $pd$ and the
$sd$ of the defender,
where ($30 \leq pd \leq
60$) and ($1 \leq sd \leq
10$).
The third test case line contains two space-separated integers
denoting the $pb$ and the
$sb$ of Bale, where
($30 \leq pb \leq 60$) and
($1 \leq sb \leq 10$).
Output
For each test case, print out YES if Bale will be ahead of the defender (offsides) at the time of the pass. Print out NO if he will not.
| Sample Input 1 | Sample Output 1 |
|---|---|
1 2 45 30 2 30 2 |
NO |
