75) a river 100 m wide flows 1 m/s due south. a boat that travels 1 m/s relative to the water is pointed due east as it crosses from the west bank. relative to its starting point, the boat travels

a) 141 m.
b) 100 m.
c) 200 m.
d) more than 200 m.
e) nowhere

A) 141 m

Explanation:

Once in water, the boat, when trying to get the opposite border traveling due east, is moved due south by the river flowing.

So, the total velocity of the boat, will be due to these both components, which are perpendicular each other.

So, we can find the magnitude of this velocity, taking into account that velocity is a vector, using trigonometry, applying Pythagorean theorem, as follows:

v² = vr² + vb² ⇒ v= √(1m/s)² +(1m/s)² =√2(m/s)² = 1.41 m/s

So, relative to its starting point, the boat travels 141 m instead of the 100m that it  would have traveled if the river had been quiet.  

A) 141 m

Explanation:

Given that the boat travels at a speed of 1m/s due east in a river that flows 1m/s due south.

Let north represent positive y axis and east represent positive x axis.

Then we can resolve the resultant velocity of the boat to vector form.

Vr = i - j ( 1 m/s on x axis and -1m/s on y axis)

The time required to travel 100m from west to east at a speed of 1m/s is;

Time t = distance/speed = 100m/1m/s = 100s

Since the boat will use 100s to cross the river, We can now determine the resultant distance after 100s:

Distance = velocity × time = (i - j) × 100 = 100i - 100j

Distance = 100i - 100j (in vector form)

Magnitude of the Resultant distance can be given as:

dr = √(dx^2 + dy^2)

dr = √(100^2 + 100^2)

dr = √(20000)

dr = 141.42m

dr = 141m

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