Exercises

 

Part 1

Response with Discussion. Clearly explain the logic behind your answers

 

1. A football player kicks a ball very high and then runs in a straight line and catches it. Which had the greater displacement, the batter or the

    ball?

 

2.  If  = + is   necessarily greater than and/or ?

 

 

3.  Two vectors have length   = 3.5 km and = 4.0 km.  What are the maximum and minimum magnitudes of their vector sum?

 

 

4.  Can the magnitude of a vector ever

 

     a. be equal to one of its components, or

 

 

     b. be less than one of its components?

 

 

5. Can a particle

 

     a. That has a constant speed be accelerating?

 

 

     b. That has constant velocity be accelerating?

 

 

6. A student sitting in an enclosed train car, moving at constant velocity, throws a ball straight up into the air in her reference frame.

 

     a. Where does the ball land?

 

     b. Where does the ball land if the train accelerates.

 

 

7.  Two rowers, who can row at the same speed in still water, start across a river at the same time. One of the rowers heads straight across

      and is pulled downstream somewhat by the current. The other one heads upstream at an angle so as to arrive at a point opposite the

      starting point. Which rower reaches the opposite side first?

 

 

Part 2: Problems in Vector Addition

 

Break each problem response into the parts shown below.

 

a. Diagram

b. Variables that are known along with values

c. Variable(s) whose values need to be found

d. Equation(s) to use

e. Calculations

 

 

1.  A bus is driven 215 km west and then 85 km southwest. What is the displacement of the bus from the point of origin (magnitude and

       direction)?

 

 

 

2.  A delivery truck travels 18 blocks north, 10 blocks east, and 16 blocks south. What is its final displacement

 

 

 

3.  If V_x = 6.80 units and V_y = -7.40 units,  determine the magnitude and direction of (Resulting vector).

 

 

4.  The components of a vector  can be written V_x, V_y, V_z.  What are the components and length of a vector which is the sum of the two

     vectors,   and whose components are (8.0, -3.7, 0.0) and (3.9, -8.1, -4.4)?

 

 

5.  Vector is 6.6 units long and points along the negative x axis. Vector  is 8.5 units long and points at +45⁰ to the positive x axis.

 

     a.  What are the x and y components of each vector?

 

     b.  Determine the sum  (magnitude and angle).

 

 

 

6.  The summit of a mountain, 2450 m above base camp, is measured on a map to be 4580 m horizontally from the camp in a direction

      32.5º west of north.

 

        a.  What are the components of the displacement vector from the camp to the summit?

 

        b.  What is its magnitude? Choose the x axis east, y axis north, and z axis up.

 

 

 

Part 3: Problems in Projectile Motion (neglect air resistance)

 

Break each problem response into the parts shown below.

 

a. Diagram

b. Variables that are known along with values

c. Variable(s) whose values need to be found

d. Equation(s) to use

e. Calculations

 

 

1.  A Jack Russell leaps horizontally (without getting hurt-she has special powers) from a 6.5-m-high rock with a speed of 3.5 m/s. How far

     from the base of the rock will she land?

 

 

 

2.  A diver running  1.8 m/s dives out horizontally from the edge of a vertical cliff and 3.0 s later reaches the water below.

 

     a.  How high was the cliff

 

     b.  How far from its base did the diver hit the water?