PROBLEM STATEMENT 1:
There is a ceiling fan
Blade 2 is along the X-axis. Blade number 1, 2 and 3 are in X-Z plane and axis of the fan is along the Y-axis. Now, a small ball is hanging at the free end of blade 2 of this ceiling fan with the help of an elastic string. Fan starts running with a constant angular acceleration α in the clockwise direction as seen from
the top along the Y-axis.
Now, due to this string makes an angle Θ and φ with the Y-axis when seen from RHS and front respectively. (Neglect air resistance)
Input:
1.) Initial length of the spring ‘l’.
2.) Distance from axis of fan to point on blade where string is attached ‘R’.
3.) Constant angular acceleration ‘α’.
4.) Angles ‘Θ’ and ‘φ’.
5.) Assume mass of ball attached with spring (say ‘m’)
6.) Spring constant ’k’=10N/cm
Output:
Plot a graph between ‘Θ’ and ‘φ’ w.r.t. time ‘t’.
PROBLEM STATEMENT 2:
UEFA Champions league was dominated by English clubs again but it was the
Spanish club Barcelona who had the last laugh. Manchester United lost the final 2-0 and they have also lost the services of Cristiano Ronaldo and Carlos Albert Tevez. Though Man U has signed Michael Owen but he along with Berbatov and Rooney need something special to overcome the stiff competition from the likes of Chelsea, Liverpool and not to forget the champions league. The club has been hit hard by the recession and so they have thought of moving away from the conventional strategy of high profile player transfers to utilizing resources of computer software for on-field play in an unprecedented manner. The job of the computer software will be to find out for a particular corner kick, which player should be actuated so that a header by the player results in a best goal.
During the practice session, they want to practice some corner kicks. There are 5 positions marked on the outer rectangle where 5 players will take their respective positions. One player will take a corner kick (i.e. from point O) with some speed and at some angle with horizontal plane and with the side line while the rest of the 5 players and the goalkeeper are allowed to move as soon as player takes acorner kick. They will run towards the ball with some velocity and try to make a perfect goal with HEADER SHOTS. Goalkeeper is standing in the middle of the goalpost and has only sufficient time to dive (no time to run) in the plane of the goalpost and cover an area corresponding to the semicircle with his height being the radius of the semicircle. If a player tries to hit the ball with his head in the remaining space (subtracting the semicircular area of dive from the projected area of goalpost), a goal is assured.
Write a program that will take as input the quantities given below and give the
output whether a goal is possible or not. And if possible, it should give as output the following quantities given below.
Inputs to the program are:
V=speed of kicking the ball.
Θ=angle of projection of ball from horizontal
Φ=angle of plane of projection of the ball from the side line.
Output must be:
“.....GOAL....”
and
1. Speed of player with which he should run.
2. Direction in which he should run (i.e. the angle in which his velocity is directed from the base line)
3. At what angle he should dive from the horizontal.
OR
“GOAL IS NOT POSSIBLE”
(considering all the 5 positions)
Assumptions:-
1. Consider minimum time from kicking the ball to the goal (i.e. crossing the
goal post) as the as the best goal.
2. While kicking the ball impact is given at its centre of mass.
3. Player dives in the direction of running.
4. No effects of wind are to be considered.
5. During the collision of the ball with head, consider it as a point mass.
6. Average height of a person =180 cm and the height of goal post is 2.44 m
while the length is 7.32 m.
7. Consider the line containing the points A,B,C,D as the base line.
8. Consider the line whose length is 70m as the side line.
9. Point C is on the intersection of arc and the side line while D is placed
exactly at the mid-point of the length between C and the end of the base
line nearer to point E.
10. Points A & B are located at the respective position as of C & D.
11. Point E is located at a distance of 4m from the end of the base line.
There is a ceiling fan
the top along the Y-axis.
Now, due to this string makes an angle Θ and φ with the Y-axis when seen from RHS and front respectively. (Neglect air resistance)
Input:
1.) Initial length of the spring ‘l’.
2.) Distance from axis of fan to point on blade where string is attached ‘R’.
3.) Constant angular acceleration ‘α’.
4.) Angles ‘Θ’ and ‘φ’.
5.) Assume mass of ball attached with spring (say ‘m’)
6.) Spring constant ’k’=10N/cm
Output:
Plot a graph between ‘Θ’ and ‘φ’ w.r.t. time ‘t’.
PROBLEM STATEMENT 2:
UEFA Champions league was dominated by English clubs again but it was the
Spanish club Barcelona who had the last laugh. Manchester United lost the final 2-0 and they have also lost the services of Cristiano Ronaldo and Carlos Albert Tevez. Though Man U has signed Michael Owen but he along with Berbatov and Rooney need something special to overcome the stiff competition from the likes of Chelsea, Liverpool and not to forget the champions league. The club has been hit hard by the recession and so they have thought of moving away from the conventional strategy of high profile player transfers to utilizing resources of computer software for on-field play in an unprecedented manner. The job of the computer software will be to find out for a particular corner kick, which player should be actuated so that a header by the player results in a best goal.
During the practice session, they want to practice some corner kicks. There are 5 positions marked on the outer rectangle where 5 players will take their respective positions. One player will take a corner kick (i.e. from point O) with some speed and at some angle with horizontal plane and with the side line while the rest of the 5 players and the goalkeeper are allowed to move as soon as player takes acorner kick. They will run towards the ball with some velocity and try to make a perfect goal with HEADER SHOTS. Goalkeeper is standing in the middle of the goalpost and has only sufficient time to dive (no time to run) in the plane of the goalpost and cover an area corresponding to the semicircle with his height being the radius of the semicircle. If a player tries to hit the ball with his head in the remaining space (subtracting the semicircular area of dive from the projected area of goalpost), a goal is assured.
Write a program that will take as input the quantities given below and give the
output whether a goal is possible or not. And if possible, it should give as output the following quantities given below.
Inputs to the program are:
V=speed of kicking the ball.
Θ=angle of projection of ball from horizontal
Φ=angle of plane of projection of the ball from the side line.
Output must be:
“.....GOAL....”
and
1. Speed of player with which he should run.
2. Direction in which he should run (i.e. the angle in which his velocity is directed from the base line)
3. At what angle he should dive from the horizontal.
OR
“GOAL IS NOT POSSIBLE”
(considering all the 5 positions)
Assumptions:-
1. Consider minimum time from kicking the ball to the goal (i.e. crossing the
goal post) as the as the best goal.
2. While kicking the ball impact is given at its centre of mass.
3. Player dives in the direction of running.
4. No effects of wind are to be considered.
5. During the collision of the ball with head, consider it as a point mass.
6. Average height of a person =180 cm and the height of goal post is 2.44 m
while the length is 7.32 m.
7. Consider the line containing the points A,B,C,D as the base line.
8. Consider the line whose length is 70m as the side line.
9. Point C is on the intersection of arc and the side line while D is placed
exactly at the mid-point of the length between C and the end of the base
line nearer to point E.
10. Points A & B are located at the respective position as of C & D.
11. Point E is located at a distance of 4m from the end of the base line.
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