ActivPhysics%20OnLine

1

• ActivPhysics OnLine
• Problem 3.3 Changing the x-velocity
• Choose xy coordinates in the usual way. y
• x
• upwards y
• downwards - y
• In these questions we are assuming there is no
  air resistance.

2

• Problem 3.3 Question 1
• What is the balls total time in the air?
• First let us find the time for the balls upward
  trajectory. Call this t.
• The balls initial velocity in the y direction is
  10 m/s, but at the highest point of the balls
  motion its velocity in the y direction is 0.

3

viy 10 m/s g -10 m/s2 v viy ay t 0
10 m/s (-10 m/s2) t 10 m/s2 t 10 m/s t
1.0 s Remember that this is the time for the
balls upward trajectory. If there is no air
resistance, then the balls path is a parabola
(which is symmetric) and the time for the balls
downward trajectory is also 1.0 s. Thus the
balls total time in the air is 2 s.

4

The balls total time in the air has the same
value 2.0 seconds and does not depend on the
velocity in the x direction because the motions
in the x and y directions are independent. The
balls total time in the air depends only on its
initial y position, its initial velocity in the y
direction, and its acceleration in the y
direction.

5

• Question 2 What is the balls maximum height?
• v2 viy 2 2 a (yf - yi )
• 0 (10 m/s)2
• 2 (-10 m/s2) (yf -0)
• 2 (10 m/s2) yf (10 m/s)2
• yf 5.0 m
• The balls maximum height has the same value 5.0
  meters, regardless of its velocity in the x
  direction, because motions in the x and y
  directions are independent.

6

• The balls maximum height depends only on the
  balls initial y position, its initial velocity
  in the y direction, and its acceleration in the y
  direction.

7

• Question 3 What is the horizontal distance or
  range that the ball travels before hitting the
  ground?
• x vx t ½ (ax t2)
• There is no acceleration in the x direction, ax
  0, and so
• x vx t.
• The horizontal range x is greater if the
  horizontal component of the balls velocity is
  greater.
• If vx 2.0 m/s,
• then x (2.0 m/s)(2.0 s) 4.0 m. If vx 10
  m/s,
• then x (10 m/s)(2.0 s) 20 m.

8

• ActivPhysics OnLine
• Problem 3.4 x- and y- accelerations of a
  projectile
• Choose xy coordinates in the usual way.
  y
• x
• Question 1 What is the acceleration in the x
  direction? Ans. Zero.

9

• Question 2 Calculate the acceleration y
  components from the graph.
• t (s) v (m/s)
• 0.0 30
• 1.0 20
• 2.0 10
• 3.0 0.0
• 4.0 -10
• a (vf vi)/ (tf ti)
• For example from 0 to 1 s
• a (20 m/s - 30 m/s)/(1s 0s)
• a -10 m/s2 In each case this same value is
  obtained.

10

• Question 3 By how much does the y-velocity
  component change in each of the following time
  intervals?
• ay -10 m/s2
• vy viy ay t
• ?vy ay t
• For t 1.0 s, ?vy -10 m/s.
• For t 2.0 s, ?vy -20 m/s.
• For t 0.1 s, ?vy -1.0 m/s.