Answer
(a) The acceleration of the elevator is $1.8~m/s^2$ (downward)
(b) The elevator's speed is $8.7~m/s$
Work Step by Step
(a) We can find the person's acceleration:
$\sum F = ma$
$mg-F_N = ma$
$a = \frac{mg-F_N}{m}$
$a = \frac{(51~kg)(9.80~m/s^2)-408~N}{51~kg}$
$a = 1.8~m/s^2$ (downward)
The acceleration of the elevator is $1.8~m/s^2$ (downward)
(b) We can find the elevator's speed:
$v_f=v_0+at$
$v_f = 1.5~m/s+(1.8~m/s^2)(4.0~s)$
$v_f = 8.7~m/s$
The elevator's speed is $8.7~m/s$
