Mary needs to row her boat across a 100m wide river that is flowing to the east at a speed of 1.0m/s. Mary can row with a speed of .0m/s

a) If mary points her boat due north, how dar from her intended landing spot will she be when she reaches the opposite shore?
B) What is her speed with respect to the shore?

v is the speed of the river

u is the speed of the boat
d is the width of the river
x=?
v/u=x/d
x=v•d/u= …
V=sqrt(v²+u²)

To solve this problem, we can break it down into two components:

a) How far from her intended landing spot will Mary be when she reaches the opposite shore?

To find the displacement in the east-west direction, we need to determine the time it takes for Mary to cross the river.

Time = Distance / Speed = 100m / 1.0m/s = 100s

During this time, the river will carry Mary downstream by a distance equal to the river's speed multiplied by the time:

Downstream distance = Speed * Time = 1.0m/s * 100s = 100m

Since Mary's intended landing spot is due north, she will be directly across from her intended spot at the opposite shore, so the displacement in the east-west direction will be 100m to the east.

b) What is Mary's speed with respect to the shore?

Mary's speed with respect to the shore is the vector sum of her rowing speed and the river's speed.

Speed with respect to the shore = √((rowing speed)^2 + (river's speed)^2)
Speed with respect to the shore = √((0m/s)^2 + (1.0m/s)^2) = 1.0m/s

Therefore, Mary's speed with respect to the shore is 1.0m/s.

To answer part (a) of the question, we need to consider the motion of the boat due to the river current. Here's how we can calculate how far Mary will be from her intended landing spot.

Let's break down the problem into two components: horizontal and vertical.

1. Horizontal Component:
The horizontal component deals with the motion of the boat due to the river current. As the river current is 1.0 m/s to the east, it means that the boat will also drift eastward at that same speed.

Therefore, the time it takes for Mary to cross the river can be found by dividing the width of the river (100 m) by her boat's velocity relative to the river current (which is 0 m/s). So, the time taken to cross the river is 100 m / 0 m/s, which is undefined (since we cannot divide by zero).

2. Vertical Component:
The vertical component deals with the motion of the boat due to Mary's rowing. Since Mary is rowing directly north (perpendicular to the current), the motion of the boat in the north direction will not be affected by the river current.

Since Mary's boat speed is 0 m/s (since she is not rowing), her boat will not move in the vertical direction. Therefore, the boat will not be displaced from its vertical position.

In summary, when Mary reaches the opposite shore, she will be directly across from her intended landing spot. However, due to the horizontal drift caused by the river current, she will be displaced eastward by the distance traveled by the river current during the crossing. But since the time for crossing is undefined, we cannot determine the exact displacement.

Moving on to part (b) of the question, we need to find Mary's speed with respect to the shore. Since the speed of the boat is defined as 0 m/s, her speed relative to the shore will also be 0 m/s.