(a) What minimum impulse must be imparted to a football of mass0.412 kg to have

Question

(a) What minimum impulse must be imparted to a football of mass0.412 kg to have a horizontal range of26.0 m?
________ kg · m/s

(b) Assuming that contact with the football is maintained as itmoves 22.0 cm, estimate the time ofcontact and the average force on the football.
time of contact = ______s average force = _____ N

time of contact = ______s average force = _____ N

Explanation / Answer

We know that            v = gR This can be derived from kinematic relation ofrange and when = 45o So that minimum impulse = mv = m * gR =0.412 * 9.8 * 26 = 6.576 kgm/s (b) S = 0.5gt2      ==> t = 2S/g               = 2 * 0.22 / 9.8                = 0.211 s (c) Force = impulse / time                 = 6.576 / 0.211                  = 31N

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