Question

Mary needs to row her boat across a 190 m -wide river that is flowing to the east at a speed of 1.3 m/s . mary can row with a speed of 3.5 m/s . part a if mary points her boat due north, how far from her intended landing spot will she be when she reaches the opposite shore?

Answer 1

Mary will be around 70.57 meters east of her intended landing point due to the river's current carrying her downstream while she rows northward.

Step-by-step explanation:

Calculating Mary's Displacement Across the River

Mary is attempting to row her boat across a river that is moving to the east while she points her boat due north. Her velocity with respect to Earth will be the vector sum of her velocity in still water and the river's current’s velocity. Given that Mary can row at a speed of 3.5 m/s and the river flows at 1.3 m/s to the east, we can calculate how far she would be from her intended landing spot when she reaches the opposite shore.

To find out how far she will be swept downstream, we must analyze the vertical and horizontal components of her velocity separately. The vertical (northward) component of her velocity is 3.5 m/s, while the horizontal (eastward) component is 1.3 m/s due to the river's current. As she is crossing the 190 m-wide river, we can calculate the time it will take her to cross:

Time = Width of river / Mary's northward speed = 190 m / 3.5 m/s = 54.29 seconds

In this time, the river will carry her eastwards:

Drift = River's speed * Time = 1.3 m/s * 54.29 s ≈ 70.57 m

Mary will therefore be approximately 70.57 meters downstream from her intended landing spot on the opposite shore.

Answer 2

If Mary is rowing at 3.5 m/s then it will take her 190 m divided by 3.5 m/s or about 54 secs to cross the river. If the river is flowing at 1.3 m/s then in 54 secs she will be carried 54 x 1.3 or around 70.5 meters downstream when she lands on the opposite shore.