A soccer ball of mass 0.4 kg is moving horizontally with a speed of 20 m/s, when

Question

A soccer ball of mass 0.4 kg is moving horizontally with a speed of 20 m/s, when it is kicked by a palyer. The kicking force is so large that the ball flies up at an angle of 30 degrees above the ground, with double the initial speed. The player however is sure that he aimed his foot at a different, much large angle above the ground. Taking the player's word to be true, calculate the magnitude as well as the direction of the average kicking force, if you are also given that the foot was in contact with ball for one hundredth of a second. Hint: make a sketch relating the initial momentum, final momentum and kicking force vectors.

Explanation / Answer

Assume that initially the ball was moving in the negative x axis.
Initial momentum, P1 = - 20 x 0.4 = - 8 i kg. m/s.
Once kicked, the ball moves with a velocity 40 m/s and making an angle 30 degree above the ground.
Final momentum, P2 = 40 x 0.4 x cos(30) i + 40 x 0.4 x sin(30) j
= [13.856 i + 8 j] kg m.s

Change in momentum = Final momentum - Initial momentum
dP = P2 - P1
=  [13.856 i + 8 j] kg m.s - ( - 8 i kg. m/s)
= [21.856 i + 8 j] kg m.s

Force = dP/dt
dt = 1/100 s
F = [21.856 i + 8 j] / (1/100)
= [2185.6 i + 800 j] N

Magnitude of force, |F| = sqrt[2185.62 + 8002]
= 2327.45 N

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.