Chapter 2 - 1D Kinematics

Question 1

Mistakes with Free Fall Problems (x2)

Answer 1

1. At max height, velocity is equal to 0
2. Displacement, if falling downards, remember that it is negative

Question 2

How to identify free fall motion problems?

Answer 2

• Gravity is only force/ignoring air resistance
• Vertical motion, “falling”, “object is dropped”, “thrown upwards”

Question 3

Suppose you are climbing in the high sierra when you suddenly find yourself at the edge of a fog shrouded cliff. to find the height of this cliff, you drop a rock from the top and 10s later, hear the sound of it hitting the ground at the food of the cliff. ignoring air resistance, how high is the cliff if the speed of sound is 330m/s.

Answer 3

1. VARIABLES
   - t is the time for the rock to fall
   - Total time is time of fall + tsound thus time of sound is 10-t
2. Calculate distance for rock using 1/2gt^2
3. Calculate distance for sound (distance = speed x time)
   d = 330(10-t)
   330(10-t) = 4.9t^2
4. Set distances equal and rearrange equation
5. Solve quadratic for time and sub this back into the distance equation

you should get 383m

Question 4

A particle begins from rest at a point +10 meters from the origin at time t = 0, and begins accelerating at
a constant 2 m/s2 in the negative direction. At time t = 4 seconds, the particle has reached a certain speed; it
stops accelerating, and continues traveling with that same speed until t = 7 seconds. What is its position
relative to the origin at t = 7 seconds?

Answer 4

first, you have to calculate the displacement after 4 seconds which should be -6

Then you calcualte the velicty after 4 seconds which is -8

Then you input into x = x0 + v0t + 1/2at^2
where x0 = 10 to find the position at 4 seconds

Then you input into x = x1 + v0t (derived again from the same equation above except that now the acceleration term is 0

you should get x2 equals -30

Question 5

The earth moves around the sun in a nearly circular orbit of radius 1.50 x 10^11 m. During
the three summer months (an elapsed time of 7.89 x 106
s), the earth moves one-fourth of
the distance around the sun. (a) What is the average speed of the earth? (b) What is the
magnitude of the average velocity of the earth during this period?

What is the difference between average speed and average velocity for these equations?

Answer 5

For average speed you find the circumstance then divide by 4 to find the distance and then divide thay by t to find the speed

for average velocity you have to consider the shortest distance for the displacement which would be a straight line. you find the hypotenuse using the radius and you should get 2.11x10^11 and then divide that by the time and obtain 2.68x10^4

Question 6

As a tennis ball is struck, it departs from the racket horizontally with a speed of 28.0 m/s.
The ball hits the court at a horizontal distance of 19.6 m from the racket. How far above the
court is the tennis ball when it leaves the racket?

Answer 6

You gotta think intuitively :)

First you want to find the tiem of flight, and you have the range and the vox = 28m/s (since it is launched horizontally so there is no voy). Time of flight is 0.7 sec, then you sub into the kinematic equation setting the final height equal to 0 and solving for the inital height, using a = 9.8

Question 7

For the kinematic equations what do you NEED to remember!!!!!

Answer 7

the v^2 and the t^2!!! CMON PLS DONT FORGET

Question 8

Spider-man steps from the top of a tall
building. He falls freely from rest to the
ground a distance of h. It takes him 1.0 s
to fall the last h/4 distance of his fall.
(a) What is the height h of the building?

Answer 8

Split up his fall into two parts, the first 3/4 and the last 1/4

First 3/4
v0 = 0 a = 9.8 y = 3/4h

v = sqrt(14.7h)

Last 1/4
v = ? a = 9.8 y = h/4 t =1
h/4 = v + 9.8/2
h/4 =sqrt(14.7h) + 4.9
Rearrange to other sides, square both sides to remove the square root, solve using the quadratic equation. You should get h = 233m or so

Question 9

If there is no acceleration, what does that say about the velocity?

Answer 9

Velocity is constant so vo is the same as v

Question 10

The x and y components can be treated separately, what does that mean for time?

Answer 10

Time is the same in both directions, so you can write equations as a function of time and then set equal to each other

Question 11

What is the angle that maximizes the distance of teh projectile?

Answer 11

45 degrees