History:
In 1853, four German nuns left their
convent in Germany to open a school.
Later on, their new convent started a
school that eventually became Mount
Saint Mary College. The four original
nuns crossed over the Hudson River on a
steamboat known as the Mary Powell,
which is the name of a famous
Newburgh family. The campus of
Mount Saint Mary College sits along
Powell Avenue.
Problem:
Find the speed and heading that the steamboat, Mary Powell, should have had in order to cross the river
straight across, assuming it took one hour to cross.
According to library.marist.edu, the average width of the Hudson River is about one mile (5,000 feet),
and according to tidesandcurrents.noaa.gov, the average current speed of the river is 1.4 knots
(approximately 2.5 feet/second).
(Not drawn to scale)
-2.5 ft/sec
5,000ft/hr
Find the speed and heading that the steamboat, Mary Powell, should have had in order to cross the
river straight across, assuming it took one hour to cross. According to library.marist.edu, the
average width of the Hudson River is about one mile (5,000 feet), and according to
tidesandcurrents.noaa.gov, the average current speed of the river is 1.4 knots (approximately 2.5
feet/second).
Solution:
The first step to solving this problem is converting our time (one hour) into seconds so everything is
measured in the same units.
1 ℎ𝑟 ×
60 𝑚𝑖𝑛
1 ℎ𝑟
= 60 𝑚𝑖𝑛 ×
60 𝑠
1 𝑚𝑖𝑛
= 3600 𝑠
Next, divide the width of the river by that time; the picture to the right illustrates the problem.
5000 𝑓𝑡
3600𝑠
= 1.389 𝑓𝑡
𝑠
Using the Pythagorean Theorem,
find what the speed of
Mary Powell should have been.
2.86 ft/sec
2.52 + 1.3892 = 𝑐 2
√2.52 + 1.3892 = 𝑐
𝑐 ≈ 2.86 𝑓𝑡
-2.5 ft/sec
𝑠
1.389 ft/sec
Convert to knots:
1.4 𝑘𝑛𝑜𝑡𝑠
2.5𝑓𝑡
𝑘
=
2.86𝑓𝑡
𝑠
𝑠
1.4 𝑘𝑛𝑜𝑡𝑠 × 2.86𝑓𝑡 = 2.5𝑓𝑡 × 𝑘
𝑠
𝑘=
1.4 𝑘𝑛𝑜𝑡𝑠×2.86𝑓𝑡
⁄𝑠
2.5𝑓𝑡
𝑠
≈ 1.6016 𝑘𝑛𝑜𝑡𝑠
⁄𝑠
The speed of the Mary Powell should be approximately 2.86 feet per second or approximately 1.6
knots.
To find the heading, use the following equation:
Tanθ =
Tanθ =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
2.5
1.389
Tanθ ≈ 1.80
θ ≈ 60.9°
The heading of the Mary Powell was approximately 𝟔𝟎. 𝟗°
Thus, in order to cross the Hudson River perfectly straight and within an hour, the Mary Powell should
have gone at a speed of 2.86 feet/second, or 1.6 knots, at a heading of around 60.9 degrees.