Answer to Question #95638 in Mechanics | Relativity for Moses

Question

1. A man start from point A and walks a distance of 3.0km due northeast to point B. from point B he then walk 4.0km due Southeast to point X. Calculate the shortest distance between point A and X.

2. Two cars A and B move with a velocity of 60km north and 40 km north respectively. What is the velocity of B with respect to A?

3. Two forces 5N and 8N act at the same point at an angle of 45 degree to each other. Calculate the magnitude of their resultant.

4. A force of 20N act at an angle of 30 degree to the horizontal. Determine the vertical component of the force.

5. The forces of magnitude 30N and 40N act at an angle of 90degree to each other. Calculate the magnitude of their resultant.

6. Two forces whose resultant is 100 N are perpendicular to each other. If the horizontal force make an angle of 60degree with the resultant. Calculate it's magnitude.

7. Two forces of magnitude 8N and 5N act at an angle of 60 degree to each other. Find the magnitude.

Answer 1

1.

$$d=\sqrt{3^2+4^2}=5.0\ km$$

2.

$$V=60-40=20\frac{km}{h}\ south$$

3.

$$F=\sqrt{8^2+5^2-2(8)(5)\cos{45\degree}}=12.1\ N$$

4.

$$F_y=F\sin{30}=(20)(0.5)=10\ N$$

5.

$$F=\sqrt{30^2+40^2}=50\ N$$

6.

$$F_1=F\cos{60}=(100)(0.5)=50\ N$$

7.

$$F=\sqrt{8^2+5^2-2(8)(5)\cos{60\degree}}=11.4\ N$$