- Ayk Week 21 Homework Due In An Hour A Group Of Children Are Standing At The Top Of A Slide Eventually Each One Will Go 1 (46.23 KiB) Viewed 72 times
- Ayk Week 21 Homework Due In An Hour A Group Of Children Are Standing At The Top Of A Slide Eventually Each One Will Go 2 (61.08 KiB) Viewed 72 times
- Ayk Week 21 Homework Due In An Hour A Group Of Children Are Standing At The Top Of A Slide Eventually Each One Will Go 3 (55.71 KiB) Viewed 72 times
C) The instantaneous speed of each child was measured as they went down the slide and recorded in the table below.. Child name Alex Berry Carmen Recorded speed 3.5 m/s 2 m/s 5 m/s Note: "Speed" is a scalar quantity that describes a change in position per unit time. "Velocity" is a vector quantity whose magnitude describes a change in position per unit time and whose direction points in the direction of motion. Speed is the norm of an object's velocity at a particular instant in time. A. Draw and label the velocity vector (V4.VB. and Vc) of each child as they went down the slide You can assume that the direction of motion of each child is parallel to the slide. Write expressions to relate the velocity vector of each child to d. (It should feel very easy to relate the velocity vectors to d since they point along the same direction as d This was the reason we defined in the first place!) D) Now you need expressions for these velocity vectors in terms of the unit vectors hand from the diagram. There are multiple ways to accomplish this goal, but you only need to do it once; choose your favorite method. (Note: the unit vector û defined the vertical direction pointing up; it is not the unit vector to define the velocity vector's direction even though they both use the symbol v.) Method 1: You have an expression from (B) that relates AF, to d and an expression from (A) that relates Ar, to and h. Substitute these expressions into the velocity expressions until you have a the velocity vectors in terms of h and û. Method 2: The velocity vectors can be written as the sum of their "projections along the h and directions (this is only true because h and are perpendicular to each other). To find a "projection of a vector" in a particular direction you should dot that vector with the unit (VA·h)h + (V₁ · û). You know vector that defines that direction. Therefore: VA = the magnitude of each velocity vector and you can do a little bit of trig and geometry to determine the angle between the velocity vectors and hand so these dot products should not be very difficult. A If you can think of an alternative method, go for it. Be sure to show all your steps and explain your work clearly.
FONTH REV HOW TO URSSIT pointing up; it is not the unit vector to define the velocity vector's direction even though they both use the symbolv.) • Method 1: You have an expression from (B) that relates Ar, to d and an expression from (A) that relates Ar, to û and ĥ. Substitute these expressions into the velocity expressions until you have a the velocity vectors in terms of ħ and v. • Method 2: The velocity vectors can be written as the sum of their "projections" along the h and û directions (this is only true because ħ and û are perpendicular to each other). To find a "projection of a vector" in a particular direction you should dot that vector with the unit vector that defines that direction. Therefore: VA = (VA·h)h + (VA). You know the magnitude of each velocity vector and you can do a little bit of trig and geometry to determine the angle between the velocity vectors and hand so these dot products should not be very difficult. If you can think of an alternative method, go for it. Be sure to show all your steps and explain your work clearly. E) Can you agree that defining the new unit vector d made it very easy to describe other vectors that pointed along the same direction as d, instead of using unit vectors that pointed horizontally and vertically? In future courses, you'll typically use the Cartesian coordinate system unit vectors that point usually point horizontally and vertically. Don't forget that it might make you life easier to define a new unit vector and use it instead!