Answer
He will emerge from the barrel with a speed of 15.5 m/s.
Work Step by Step
$K_2 + U_2 = \frac{1}{2}kx^2 + W_f$
$\frac{1}{2}mv^2 + mgh = \frac{1}{2}kx^2 - F_f~d$
$v^2 = \frac{kx^2 - 2F_f~d - 2mgh}{m}$
$v = \sqrt{\frac{kx^2 - 2F_f~d - 2mgh}{m}}$
$v = \sqrt{\frac{(1100~N/m)(4.0~m)^2 - (2)(40~N)(4.0~m) - (2)(60~kg)(9.80~m/s^2)(2.5~m)}{60~kg}}$
$v = 15.5~m/s$
He will emerge from the barrel with a speed of 15.5 m/s.
