Motion in 2D
Component Vectors
Find the missing component vectors by drawing the triangle and using sin/cos. Show all your work.
1.
Initial velocity of 10 m/s at an angle of 13 degrees above horizontal.
1.
2.
vy =
Initial acceleration of 5.5 m/s2 at an angle of 79 degrees above horizontal.
1.
3.
vx =
ax =
ay =
Total displacement is 90 m at an angle of 45 degrees above horizontal.
1.
dx =
dy =
Using Component Vectors to Solve Motion Problems in 2D
Use the idea of component vectors to solve the following problems. Show all your work.
4.
A rocket is traveling at a constant 100 m/s at an angle of 50 degrees above horizontal. What is the
rockets velocity in the x-direction? Y-direction? How far in the x-direction has it traveled in 20
minutes? How far in the y-direction has it traveled? What are the rocket’s grid coordinates after 40
minutes? (assume the motion is a constant velocity, far away from Earth’s gravitational pull)
5.
A yacht is cruising at a steady 6 m/s at an angle of 15 degrees north of due east. How long does it
take for the yacht to travel 10 km east of it’s original position? How far north is it then?
6.
An artillery shell strikes an enemy position moving at 175 m/s horizontally and 100 m/s
downward. What was the angle of impact?
Putting it All Together With the Distance Formula
7.
A baseball player hits a baseball with an initial velocity of 35 m/s at an angle of 50 degrees above
horizontal with an initial height of 1 meter. The outfield field fence is 370 feet away (1 foot =
0.305 meters) and 6 meters high. Is the hit a homerun? Where does the ball land?
Step one: Draw a picture on a reference frame (coordinate grid is best). Label everything you can.
Step two: Determine the initial velocity of the ball for both the X and Y components.
Step three: Write out the full distance formulas IN THE Y DIRECTION for the ball to determine how
many seconds it takes to reach the final height. Solve using the quadratic formula. You will get two
answers so make sure you think about which number you want.
Step four: Using the X direction distance formula, determine the position of the ball in the X direction
when it lands. Use that information to determine if the hit is a homerun or not.