Question

a sailboat on a lake sails 40. meters north and then sails 40. meters due east. compared to its starting position, the new position of the sailboat is (1) 40. m due east (2) 40. m due north (3) 57 m northeast (4) 80. m northeast
2018 *1. which combination correctly pairs a vector quantity with its corresponding unit? (1) weight and kg (2) velocity and m/s (3) speed and m/s (4) acceleration and m²/s
the scaled diagram below represents two forces acting concurrently at point p. the magnitude of force a is 32 newtons and the magnitude of force b is 20. newtons. the angle between the directions of force a and force b is 120°. 51. determine the linear scale used in the diagram. 52.

Explanation:

Step1: Analyze the sailboat's movement

The sailboat moves 40 meters north and 40 meters east. This forms a right - angled triangle. We can use the Pythagorean theorem to find the distance from the starting point.
Let \(a = 40\)m (north - ward displacement) and \(b = 40\)m (east - ward displacement). The distance \(d\) from the starting point is \(d=\sqrt{a^{2}+b^{2}}\).
\[d=\sqrt{40^{2}+40^{2}}=\sqrt{1600 + 1600}=\sqrt{3200}=40\sqrt{2}\approx57\]m. The direction is northeast.

Step2: Analyze vector - quantity and unit pairs

• Weight is a force, and its unit is N (newtons), not kg (mass unit).
• Velocity is a vector quantity, and its SI unit is m/s.
• Speed is a scalar quantity, not a vector quantity.
• Acceleration's unit is \(m/s^{2}\), not \(m^{2}/s\).

Step3: Analyze the force - diagram for scale determination

If we assume a length on the diagram represents a certain force magnitude. Let's say a length \(l\) on the diagram represents a force \(F\). We can find the scale by looking at the known force magnitudes and their corresponding lengths on the diagram. For example, if a 20 - N force is represented by a length of \(x\) cm, then the scale \(s=\frac{20\ N}{x\ cm}\).

Answer:

For the sailboat question: (3) 57 m northeast
For the vector - quantity question: (2) velocity and m/s
For question 51: Need more information from the diagram (such as the length corresponding to a known - force magnitude) to determine the linear scale.
For question 52: No question content provided for 52.