A soccer match is being decided with a penalty. The player kicked the ball, but

Question

A soccer match is being decided with a penalty. The player kicked the ball, but it deflected sideways from its ideal parabolic trajectory right before going into the goal, hitting the pole and causing the team to lose. Some fans of the team, who did not take this class, have been drinking and are known to be very bad losers, are giving the following explanations for the defeat: Person A The coach of the opposite team was standing 3m near the pole and his "bad gravitational presence attracted the ball, deflecting it causing our loss" (The coach has a mass of 80 kg) Person B: The winning team parked a 20 000 kg truck next to the playing field, 20 meters away from the ball They must have done it on purpose to deflect the ball. Person C The planets are probably aligned against him. It's probably Jupiter, the most massive, that messed his shot" (Mass of Jupiter is 1.898 x 10*27 kg and its located 588 million kilometers away from Earth during its closest approach) Person D: The Sun was setting on the side of the field where the ball deflected to. The Sun has a huge mass and it is even capable of producing tides, so the Sun must have done it." (Solar mass is 1.989 × 10A 30 kg, and the average Earth-Sun distance is approximately 149.6 million km) Person E The player is a Scorpius and this is a bad day for him because Antares of Scorpius is in a bad position in the sky and must have deflected the ball. Antares of Scorpius is a red supergiant with a radius of 680 times that of the sun and 12 solar masses, located SS0 light-years away from Earth

Explanation / Answer

we would sort out the matter by numerically calculating the approximate force that the said explanation can explain on the football

a. for the coach, m = 80 kg, d = 3 m

hence

F = Gm*0.5/3^2 = 29.644*10^-11 N

b. for the truck, m = 20,000 kg, d = 20 m

F = Gm*0.5/20^2 = 166.75*10^-11 N

c. for jupiter, m = 1.898*10^27 kg, d = 588*10^9 m

F = 18307.852 *10^-11 N

d. for sun, m = 1.989*10^30 kg, d = 149.6*10^9 m

F = 147376739.04 *10^-11 N

e. for scorpius, m = 12*1.989*10^30 kg, d = 550*3*10^8*24*60*60*365

F = 2.93*10^-17 N

f. for blackj holes

m = 17*10^9*1.99*10^30 kg

d = 250*10^6*3*10^8*365*24*60*60 m

F = 2.0157*10^-19 N

g. Cd = 0.25

Cd = D/0.5*1.225*A*v^2

v = 5 m/s ( assume)

A = cross sectoin area of football = pi*r^2 ( where r = 0.11 m)

D = 0.14551955 N

hence

none of therse below 1N forces can actually deviate the ball with accelerations greater than 0.2 m/s/s and hence none of these forces are responsible for the deviated trajectory of the football

we would sort out the matter by numerically calculating the approximate force that the said explanation can explain on the football

a. for the coach, m = 80 kg, d = 3 m

hence

F = Gm*0.5/3^2 = 29.644*10^-11 N

b. for the truck, m = 20,000 kg, d = 20 m

F = Gm*0.5/20^2 = 166.75*10^-11 N

c. for jupiter, m = 1.898*10^27 kg, d = 588*10^9 m

F = 18307.852 *10^-11 N

d. for sun, m = 1.989*10^30 kg, d = 149.6*10^9 m

F = 147376739.04 *10^-11 N

e. for scorpius, m = 12*1.989*10^30 kg, d = 550*3*10^8*24*60*60*365

F = 2.93*10^-17 N

f. for blackj holes

m = 17*10^9*1.99*10^30 kg

d = 250*10^6*3*10^8*365*24*60*60 m

F = 2.0157*10^-19 N

g. Cd = 0.25

Cd = D/0.5*1.225*A*v^2

v = 5 m/s ( assume)

A = cross sectoin area of football = pi*r^2 ( where r = 0.11 m)

D = 0.14551955 N

hence

none of therse below 1N forces can actually deviate the ball with accelerations greater than 0.2 m/s/s and hence none of these forces are responsible for the deviated trajectory of the football

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