Question

A treasure map instructs you to walk (25.0+A) m south, followed by (18.0+B) m east, then 64.5 m north, and finally 28.5 m east. Determine the magnitude of your total displacement, if you follow these instructions. Calculate the answer in meters (m) and rounded to three significant figures. A=8 B=68

A boat traveling at (7.50+A) m/s relative to the water aims to go straight across a river. If the river is (54.0+B) m wide and the current in the river is 3.50 m/s, how far downstream will the boat land on the other side of the river? Calculate the answer in meters (m) and rounded to three significant figures. A=8 B=68

Answer 1

Given is:-

A= 8m and B=68m

1. 25+8 = 33m south

2. 18+68 = 86m east

3. 64.5m north

4. 28.5m east

Thus the diagram will be

We have to find the length x in the above figure because displacement is the shortest distance between initial point and the final point.

Now we have created a right triangle, to find the hyponteuse of the right triangle(x) we have to use the pythagorous theorem

The base of the above triangle is b = 86+28.5 = 114.5m

the altitude of the triangel is h = 64.5-33 = 31.5m

Thus according to the pythagorous theorem

or

Thus the magnitude of the displacement is