7.5. Vector Projection http://www.ck12.org
The components of the father’s force vector is 100<cos 39◦,sin 39◦>and the “onto” vector is any vector horizon-
tally to the right. Since we are only looking for the length of the horizontal component and you already have the
angle between the two vectors, the scalar projection is:
100 ·cos 39◦≈ 77. 1 lb
Practice
- Sketch vectors< 2 , 4 >and< 2 , 1 >.
- What is the vector projection of< 2 , 4 >onto< 2 , 1 >? Sketch the projection.
- Sketch vectors<− 2 , 1 >and<− 1 , 3 >.
- What is the vector projection of<− 1 , 3 >onto<− 2 , 1 >? Sketch the projection.
- Sketch vectors< 6 , 2 >and< 8 , 1 >.
- What is the vector projection of< 6 , 2 >onto< 8 , 1 >? Sketch the projection.
- Sketch vectors< 1 , 7 >and< 6 , 3 >.
- What is the vector projection of< 1 , 7 >onto< 6 , 3 >? Sketch the projection.
- A box is on the side of a hill inclined at 30◦. The weight of the box is 40 pounds. What is the magnitude of the
force required to keep the box from sliding down the hill? - Sarah is on a sled on the side of a hill inclined at 60◦. The weight of Sarah and the sled is 125 pounds. What is
the magnitude of the force required for Sam to keep Sarah from sliding down the hill. - A 1780 pound car is parked on a street that makes an angle of 15◦with the horizontal. Find the magnitude of
the force required to keep the car from rolling down the hill. - A 1900 pound car is parked on a street that makes an angle of 10◦with the horizontal. Find the magnitude of
the force required to keep the car from rolling down the hill. - A 30 pound force that makes an angle of 32◦with an inclined plane is pulling a box up the plane. The inclined
plane makes a 20◦angle with the horizontal. What is the magnitude of the effective force pulling the box up the
plane?