Question -1:
Baseball is an interesting game consisting of two
teams-batters’ team and fielder team. At any time there are three fielders, one
catcher and one pitcher from the fielding team while two batters one at home
base and the other at 2nd base. The height of players h=6 feet .The dimensions
of field and the positions of the fielders are given in figure
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p1 = (45, 45) p1 Ã pitcher
p2, b1 = (0,
0) p2Ã catcher : b1Ã batter at home base
p3 = (100,
35) p4 = (160, 160) b2 = (90, 90) b2Ã runner at 2nd base p5 = (35, 100) all dimensions in feet.
Consider pitcher throwing ball
along AO. The ball hits the bat horizontally with batter swinging the bat in
horizontal plane in the line of hit. Coefficient of restitution for hit is
e=.75 . After the hit the ball follows projectile motion. If a fielder
(pitcher, catcher) reaches the landing position before the ball lands, its
catch out. Otherwise he has to give throw to suitable base ahead of batter(or
the runner). Find a program with following entries:
(i) Speed of ball just before
hit, v
(ii) Speed of players(fielders
and batters), vp
(iii) Angle of pitching with
normal to bat, phi
And give the solution to find
(give the output as):
(i) Speed of ball and Angle
with normal to bat after it leaves the bat,v1 & phi1
(ii) Whether its foul, f0
(iii) Or its catch out, c0
(iv) if not , c1
(a) which fielder(or pitcher,
catcher) runs to fielding, (p1/p2..) .
(b) to which base it throws the
ball, (O/B/C/D) and
(c) total time of ball journey
from hitting time to instant it reaches the base, tp
Assumptions:
(i) the ball hits the bat at
height equal to height of players.
(ii) the hit takes place in
horizontal plane containing the initial horizontal velocity of pitching.
(iii) the bat is stationary and
very massive wrt ball.
(iv) velocity of all
players(batters+fielders) are same.
(v) a fielder is able to make a
catch at any height between ground to its own height.
(vi) If ball goes beyond the
foul line its foul but catch can be made in foul zone too.
Programs in
C,C++,MATLAB.
Question -2:
Problem Statement:
Design a free flight aircraft capable of flying by its
own once launched. It should remain airborne for maximum time
and cover a maximum horizontal distance. It should be
capable of performing a few basic manoeuvres.
Arena:
Participants would have to hand launch their aircraft
from a pre specified launching zone.
You can launch your aircraft in any direction.
The launching zone would be platform of approximately 2
metres in height.
Rules:
· The aircraft should have a maximum wingspan
of 50 centimetres.
· There is no weight limit.
· You can use any material of your
choice, though we would prefer Balsa wood.
· It should not have a wingspan too
small compared to the length of the fuselage. Below is the illustration:
·
You can use any launching method.
·
Use of launching mechanisms is allowed, provided it should only provide
initial thrust. After launching, it should fly on its own.
·
You can use any aerofoil of your choice.
·
Use of any electronics on the aircraft is strictly prohibited.
·
You can do any on the spot changes on your aircraft provided it lies within
the provided specifications.
·
If your aircraft breaks at any point of the competition, you will be
eliminated from that particular round, and the team will be awarded points it scored
just before breaking. Hovewer, you are still eligible for the next round after
repairing your aircraft making a new one.
·
There is no negative point at any point of the competition.
·
If any team is found not following above rules will be disqualified immidiately.
You have to fly your aircraft for maximum range and flight time.
The point system is as follows:
R=Range(Horizontal displacement between launch point and
landing point, in metres)
T=Time of flight(Total time your aircraft is airborne, in
seconds)
You have to perform some basic manoeuvres by your aircraft. Some of them
are listed below:
Vertical Loop
Horizontal Loop
You can also perform any other manoeuvres of your choice, on which extra
points will be given.
Example:
The point system is as follows:
V=Points for vertical loop (out of 10)
H=Points for horizontal loop (out of 10)
E=Points for extra manoeuvres you perform, if any(out of
10)
*if you perform only above two manoeuvres, E=0 points.
You have to pass your aircraft from a vertical square of dimensions:
4mtr*6mtr from a distance of 10 metres. You will be given 5 minutes, in that
you can do as many passes as you can. You will be given 5 points for each pass.
P=5*number of passes
You have to land your plane as close to the landing zone as possible. The
distance from the landing zone and
launching zone will be 15 metres.
You will be given 3 chances out of which best will be entertained.
D= distance in metres from the landing spot to the point
you land, measured from tail or tip whichever is nearest.
L=25-D
Total Points: R+T+V+H+E+P+L
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