1. Draw, and label, a vector that represents the velocity, v, of an object at a direction that is 45.0 North of East.

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1 PHYSICS 2-DIMENSIONAL MOTION 1. Draw, and label, a vector that represents the velocity, v, of an object at a direction that is 45.0 North of East. 2. Draw and label the components v x and v y for the vector drawn in #1 above. Write an equation solving for v x and another equation solving for v y based on the diagram you have created in #1. 1-Dimensional Motion can be described using scalar components and (+) or (-) signs to show direction based on our coordinate system of either x or y. 2-Dimensional Motion uses both x and y to fully describe the motion of objects such as a rocket ship with horizontal and vertical thrusters. Equations for 2-Dimensional Motion Under Constant Acceleration Horizontal Component v fx = v ix + a x t x = 1 2 (v ix + v fx )t x = v ix t a x t2 v 2 fx = v 2 ix + 2a x x Independent from one another Vertical Component v fy = v iy + a y t y = 1 2 (v iy + v fy )t y = v iy t a y t2 v 2 fy = v 2 iy + 2a y y In any case, the horizontal and vertical components of the object s motion are treated independently and then added as vectors. Projectile motion differs from the above in the following manner: If air resistance is neglected, the x component of velocity does not change through out the motion of the object. The y component of the velocity, which is independent of the x component, changes by g. This describes the motion of things such as a shiny ball that rolls off of a table at a constant rate or a baseball that is thrown through the air.

2 If a shiny ball were to move with a constant velocity in the +x direction it would have a motion diagram similar to the top part of the diagram below. If the shiny ball were dropped from rest it would accelerate downward at the rate of g and would have a motion diagram similar to the left side of the diagram below. Sketch the location of the ball at each second of time if the shiny ball moves in both the x and y directions simultaneously. Draw and label v x, v y, and v.

3 The following diagram sums up the ideas of projectile motion: Horizontal *v x is constant *x gives range *Range depends on time in the air t is common link to both. Vertical *v y is changing by g *v y is responsible for changes in v *y determines t of travel. v x = v x = x t All Uniform Acceleration Equations are valid. Let s practice and apply these concepts: Suppose we have a rather shiny, happy, ball (SHB) that rolls across a level horizontal table at a constant velocity of m/s. A. How far can the SHB travel horizontally in 1.00 s? Draw a vector diagram (includes labels) and show your work. B. If the SHB rolls off of the table, and time starts the instant it leaves the edge, how far can the SHB fall vertically in 1.00s? Draw a vector diagram (includes labels) and show your work. C. What will be the resultant displacement of the SHB at a time of 1.00 s? Draw a vector diagram (includes labels) and show your work.

4 D. What will be the vertical component of the SHB s velocity at a time of 1.00 s? Draw a vector diagram (includes labels) and show your work. E. What will be the resultant velocity of the SHB at a time of 1.00 s? Draw a vector diagram (includes labels) and show your work. F. How long will it take the SHB to hit the ground if the table is 1.20 m above the floor? Draw a vector diagram (includes labels) and show your work. G. How far will the SHB be from the base of the table when it hits the floor? Draw a vector diagram (includes labels) and show your work. H. What will be the velocity of the SHB the instant before it hits the floor? Draw a vector diagram (includes labels) and show your work.

5 A projectile that is launched upward at some angle to the horizontal takes on a motion diagram similar to the one below. Note that we will neglect air resistance at this time. Draw the resultant velocity vectors on each of the positions and label v x, v y, and v. If air resistance is neglected, we see a symmetrical path in which the time to get to the maximum height is equal to the time to get back down from it. Also the initial speed at the bottom is equal to the final speed when it lands. What is the resultant velocity equal to at the maximum height of its trajectory? Now let s consider an SHB that is launched from ground level into the air at an angle that is 35.0 above the horizontal axis with an initial speed of 13.5 m/s. A. How high will the SHB reach? Draw a vector diagram (includes labels) and show your work. B. How long will the SHB remain in the air? Draw a vector diagram (includes labels) and show your work.

6 C. How far will the SHB land from its launch site? Draw a vector diagram (includes labels) and show your work. D. What will be the velocity of the SHB the instant before it impacts the ground? Draw a vector diagram (includes labels) and show your work.