Thursday 17 Sep:

 

Key Concept(s) Today:  Motion equations

 

Journal: Q

1. If you add two vectors (3 m and 5 m), which of the following can the magnitude of the resultant vector be (explain):

a.  8 m only

b.  2 m and 8 m only

c. Something else, explain.

 

 

 

http://www.youtube.com/watch?v=dxf8V7hYBt0&feature=channel

(unsolved mysteries of the universe)

 

 

More Practice Problems:

 

 

 

 2. What happens if the acceleration of an object is always directed

a) same direction as velocity.

b) perpendicular to its velocity

c) opposite direction to its velocity

i)       the object is speeding up.

ii)       the object is slowing down.

iii)       the object is turning.

iv)       this situation would not be physically possible.

 

 

 

 

 

 

 

 

 

 

a)  i

b) iii

c) ii

 

 

 

 

3. If vector A = 5 m north and vector B = 10 m east, find the resultant of vector (polar form).

 

 

 

 

 

 

 

 

 

 

 

 Ans =   11.2m ∟26.50

 

 

 

4. A girl throws a rock horizontally, with a velocity of 50 m/s, from a bridge.  It falls 80 m to the water below.  How far does the rock travel horizontally before striking the water?

 

 

 

 

 

 

 

 

 

 

 

 

 

x = Vot + 1/2 at2

80 = 0 + 1/2(10)t2 --> t =4s 

d= vt  --> (50)(4) = 200m

 

5. A jumper in the long-jump goes into the jump with a speed of 8 m/s at an angle of 30° above the horizontal. 

a. How long is he in the air?

b. How high is the apex?

c. How far does the jumper jump?

 

 

 

 

 

 

 

 

 

a.  Vy = (sin30)(8) = 4 --> Vf = Vo + at --> -4 = 4 + (-10)t 

--> t = 0.8s

b. x = Vot + 1/2 at2 --> = 4(.4) + 1/2(-10)(.42 ) --> .8m

c. d= vt --> (cos30)(8)(.8) = 5.54m

 

 

 

6. An object is thrown upward with a speed of 20 m/s on the surface of planet "E"  where the acceleration of gravity is 4.0 m/s2.  How long does it take for the object to reach maximum height?

 

 

 

 

 

 

 

 

 

 

 

 

Vf = Vo + at

 0 = 20 + (-4)t --> t = 5s

 

 

 7. A ball traveling at  15 m/s is bounced off the ground and rebounds in opposite direction at 10 m/s. If the ball is in contact with the ground for 0.04 ms, what is the average acceleration of the ball during this time interval?

 

   

 

 

 

 

 

 

 

 

 

 

         a = DV/t

               -10 -(15) / .04 = 625m/s2

 

8. A toy boat running through the water at 8.7 m/s goes directly across a stream flowing at 5.0 m/s. 

a. The angle between the heading and the course is?

b. The speed of the boat across the river bottom is?

 

 

 

 

 

 

 

 



 a. 300

b. 10m/s

 

 

 

 

 

9. What is the result (polar) of the following three vectors:
                    

 

  

 


 

      100 @ 900

 

                                                      90 @ 00

 

                                                                      200 @ 340 0

 

 

 

 

 

 

 

 

 

 

  280 ∟6.60

 

 

 

 

 

 

10. What is the result (polar) of the following three vectors:

 


 

                                                        100 @ 600

 

               200 @ 1800

 

 

                                                           100 @ 3150

 

 

 

 

 

 

 

 

 80.9 ∟168.70

 

 

 

 

 

11. A golf ball is hit with an initial speed of 100m/s.  (At a 700 angle)  (no air friction)

 

            a. How long (t) to the Apex?

            b. How high (m) to the Apex?

            c. It hit the green ----- m away

 

 

 

 

 

 

 

 

 

 

 

 

 

                       

a. Time to apex:  (depends only on vertical velocity)

 

                     Vy = (Sin q)(100) = (Sin 70)(100) = 94m/s à /10

à 9.4s  to apex

 

 

b) Heighty = Vot + ½ at2 

               Heighty = (94)(9.4)+ .5 (-10)(9.42)

                Heighty = (884) + (- 442)  = 442m

 

       c) Horz V = (Cos q)(100)   

                                                Vx  à  (Cos 70)(100) à 34 m/s

             

dist =  v (2t)    

        = (34)(18.8)  =   640m

 

 

 

 

 

 

 

 

Free-Body Exercises: Linear Motion

In each case the rock is acted on by one or more forces. All drawings are in a vertical plane, and friction is negligible except where noted. Draw accurate free-body diagrams showing all forces acting on the rock. LM-1 is done as an example, using the "parallelogram" method. For convenience, you may draw all forces acting at the center of mass, even though friction and normal reaction force act at the point of contact with the surface. Please use a ruler, and do it in pencil so you can correct mistakes. Label forces using the following symbols: w = weight of rock, T= tension, n = normal reaction force,/= friction.