Physics baseball question

Question

A 2.35 Kg baseball approaches a batter with a speed of 30 m/sec. The bat makes contact with the ball for 0.082 seconds. What is the average force that was applied by the bat if the ball moves away with a 43 m/sec speed?

Answer 1

F = I/Δt where Δt =.082 s to find I use the law of cosines and so I² = p_i² + p_f² -2 p_ip_f cosΘ in this problem Θ is 180º so now I² = ( 2.35* 30)² + ( 2.35* 43)² -2 (2.35)² (30)(43)(-1) and so I² = 4970.25 + 10211.1 +7124.03 which gives I² = 22305.375 and I = 149.34 Ns Then F= 149.349Ns/ .082s and F = 1821.34N