1. Draw the x and y components of the velocity vector below.
A vector can also be resolved into x and y components.
2. Draw the x and y components of the velocity vector below.
Vector components can be drawn along any set of axes.

3. The following depicts a force applied to a lawnmower.
Forces are often resolved into horizontal and vertical components.
Draw the horizontal and vertical components of the applied force.
4. The following shows the force of gravity acting on a box at rest on a ramp.
Force components are often drawn parallel to or perpendicular to a slope.
Draw the components of gravity that are parallel (Fx) and perpendicular (Fy) to the slope.

5. A lifeguard standing on a tower throws a buoy to a swimmer 5 m from the tower. The lifeguard, positioned 3 m above the water, pulls in the rope at a speed of 1 m/s. How fast is the swimmer coming to shore when he is 4 m from the water's edge?

6. A vector in the xy plane has a magnitude of 25 m and an x component of 12 m. The angle the vector makes with the positive x axis is:

7. The silhouette of a Christmas tree is an isosceles triangle. The angle at the top of the triangle is 30º, and the base measures 2 meters across. How tall is the tree?

8. Two billiard balls are rolling on a flat table. one has the velocity components Vx = 1.0 m/s, Vy = 2.0 m/s the other has the velocity components Vx = 2.0 m/s, Vy = 3.0 m/s. If both balls start at the same point what is the angle between their paths?

9. You are given a vector in the xy plane that has a magnitude of 70.0 units and a y component of -55.0 units. What are the two possibilities for its x component?

10. The press box at a baseball park is 36.0 ft above the ground. A reporter in the press box looks at an angle of 14.5 degrees below the horizontal to see second base. What is the horizontal distance from the press box to second base?

11. A whale comes to the surface to breathe, and then dives at an angle of 19.0 degrees below the horizontal. If the whale continues in a straight line for 140m, a)How deep is it and b)How far has it traveled horizontally?

12. A jetliner is moving at a speed of 245 m/s. The vertical component of the plane's velocity is 40.6 m/s. Determine the magnitude of the horizontal component of the plane's velocity.

13. Given 2 vectors:
A = Ax+Ay
B = Bx+By

Ax=4, Ay=2, Bx=2, & By=3

Find the z component of A * B. Find the angle between A and B.

14. When held vertically a meter stick casts a shadow 55 cm long. An hour later the shadow is just 29 cm long. Based on these measurements, how long should a day last (in hours). Why the discrepancy with respect to a real day?

ANSWERS

For solutions to all the problems on this page click here.

14.

Initially the sun was at an angle of tan^-1(1 / 0.55) = 61.2 º above the horizon.

An hour later, the sun was at an angle of tan^-1(1 / 0.29) = 73.8 º above the horizon.

The sun appears to be traveling 12.6 º per hour.

To travel 360º at this rate would take the sun 360 / 12.6º = 28.5 h

The discrepancy arises because the Sun does not pass directly over head. The Earth's axis of rotation is tilted. The shadow is longer at noon than it would be if the Sun passed directly over head, so the angle does not change as quickly.

For solutions to all the problems on this page click here.