Vector Worksheet

Show calculations on a separate piece of paper to be turned in as a group.

1. Your ship can make 10 miles per hour but the river flows at 5 mph. What is your speed relative to the shore going (a) upstream (b) downstream?

2. You run at 5 mph on a treadmill but get nowhere. Why?

3. Your airplane flies north at 120 mph, while a wind blows from the west at 50 mph.

(a) What is your "ground speed" V, relative to the land below?

(b) Could you find the angle your path makes relative to the north direction? (Call the angle x).

3. Suppose you are given a vector in the plane (on a sheet of paper, on the map, etc.)

(a) What does it mean to resolve it into its components"?

(b) Why would we want to do that--say, to find the ground speed of an airplane, in an actual situation?

4. An airplane flies at 120 mph in a direction 17.13° westward of north (towards the north-west). The wind blows at 50 mph towards the south-east, 45° off the due-east direction. In what direction does the airplane move, and how fast? (Let V be the airplane's velocity, W the wind's velocity, and let us resolve these vectors in an (x,y) system with the x-axis pointing due east and the y-axis due north).

5. Pyramid builders drag a block of stone weighing 1 ton (1000 kg) up a ramp with a 5° slope. Neglecting friction (the block moves on smooth rollers), what is the force they pull against? (hint: They have to overcome the component of the weight parallel to the surface of the ramp).