Answer
(a) Mary will be 50 meters from her intended landing spot.
(b) v = 2.2 m/s
Work Step by Step
(a) We can find the time it takes to row across the river.
$t = \frac{d_n}{v_n} = \frac{100~m}{2.0~m/s}$
$t = 50~s$
We can find the distance to the east that the river will push Mary's boat in this time.
$d_{e} = v_e~t = (1.0~m/s)(50~s)$
$d_{e} = 50~m$
Mary will be 50 meters from her intended landing spot.
(b) We can find the boat's speed with respect to the shore.
$v = \sqrt{(v_n)^2+(v_e)^2}$
$v = \sqrt{(2.0~m/s)^2+(1.0~m/s)^2}$
$v = 2.2~m/s$
