SPH4U: Practice Problems Today

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SPH4U Practice ProblemsTodays Agenda
Run and Hide
2
Understanding
An object thats moving with constant speed
travels once around a circular path. Which of the
following is/are true concerning this motion? I
The displacement is zero II The average speed
is zero III The acceleration is zero

1. I only
2. I and II only
3. I and III only
4. III only
5. II and III only

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Understanding

• Which of the following is/are true?
• If an objects acceleration is constant, then it
  must move in a straight line.
• If an objects acceleration is zero, then its
  speed must remain constant.
• If an objects speed remains constant, then its
  acceleration must be zero.

1. I and II only
2. I and III only
3. II only
4. III only
5. II and III only

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Understanding
A baseball is thrown straight upward. What is the
balls acceleration at its highest point?
Gravity is always turned on.

1. 0
2. ½ g down
3. g down
4. ½ g up
5. g up

5
Understanding
How long would it take a car, starting from rest
and accelerating uniformly in a straight line at
5 m/s2, to cover a distance of 200m?
Hint

1. 9.0 s
2. 10.5 s
3. 12.0 s
4. 15.5 s
5. 20.0 s

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Understanding
A rock is dropped off a cliff and strikes the
ground with an impact of 30 m/s. How high was the
cliff?
We need both the initial and final velocity in
the equation
Hint

1. 15.0 m
2. 20 m
3. 30 m
4. 46 m
5. 60 m

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Understanding
A stone is thrown horizontally with an initial
speed of 10 m/s from a bridge. If air resistance
could be ignored, how long would it take the
stone to strike the water 80 m below the bridge?
We need only think about the vertical components.
Hint

1. 1 s
2. 2 s
3. 4 s
4. 6 s
5. 8 s

8
Understanding
A soccer ball, at rest on the ground, is kicked
with an initial velocity of 10 m/s at a launch
angle of 300. Calculate its total flight time,
assuming air resistance is negligible?
We need only think about the vertical time to
travel up to its max height, then double it.
Hint

1. 0.5 s
2. 1 s
3. 1.7 s
4. 2 s
5. 4 s

9
Understanding
A stone is thrown horizontally with an initial
speed of 30 m/s from a bridge. Find the stones
total speed when it enters the water 4 seconds
later?
We need only think about the vertical time to
travel to find vertical speed, then combine with
horizontal speed
Hint

1. 30 m/ s
2. 40 m/s
3. 50 m/s
4. 60 m/s
5. 70 m/s

10
Understanding

• Which of the following statements is true
  concerning the motion of an ideal projectile
  launched at an angle of 450 to the horizontal?

1. The acceleration vector points opposite to the
   velocity vector on the way up and in the same
   direction as the velocity vector on the way down.
2. The speed at the top of the trajectory is zero.
3. The objects total speed remains constant during
   the entire flight.
4. The horizontal speed decreases on the way down.
5. The vertical speed decreases on the way up and
   increases on the way down.

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Understanding
This question concerns the motion of a car on a
straight track the cars velocity as a function
of time is plotted below

1. Describe what happened to the car at time t1 s
2. How does the cars average velocity between time
   t0 sand t1 s compare to its average velocity
   between times t1 s and t5 s?
3. What is the displacement of the car from time t0
   to time t7s?
4. Plot the cars acceleration during this interval
   as a function of time.
5. Plot the objects position during this interval
   as a function of time. Assuming that the car
   begins at s0.

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Understanding
This question concerns the motion of a car on a
straight track the cars velocity as a function
of time is plotted below

1. Describe what happened to the car at time t1 s

The cars velocity remains at 20 m/s, but the
acceleration changes from positive to negative at
this time (the foot leaves the accelerator)
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Understanding
This question concerns the motion of a car on a
straight track the cars velocity as a function
of time is plotted below

• How does the cars average velocity between time
  t0 sand t1 s compare to its average velocity
  between times t1 s and t5 s?

Between t0 and t1 the average velocity is ½(0
m/s 20 m/s)10 m/s Between t1 and t5 the
average velocity is ½(20m/s 0m/s)10 m/s
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Understanding
This question concerns the motion of a car on a
straight track the cars velocity as a function
of time is plotted below

• What is the displacement of the car from time t0
  to time t7s?

Displacement is the net area between the graph as
the time axis Area1/2(520) ½(210) 40m
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Understanding
This question concerns the motion of a car on a
straight track the cars velocity as a function
of time is plotted below

1. Plot the cars acceleration during this interval
   as a function of time.

16
Understanding
This question concerns the motion of a car on a
straight track the cars velocity as a function
of time is plotted below

1. Plot the objects position during this interval
   as a function of time. Assuming that the car
   begins at s0.

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Understanding

• A cannonball is shot with an initial speed of 50
  m/s at a launch angle of 400 toward a castle wall
  220m away. The height of the wall is 30 m. Assume
  that effects due to the air are negligible.
• Show that the cannonball will strike the wall.
• How long will it take for the cannonball to
  strike the wall?
• At what height above the base of the wall will
  the cannonball strike?

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Understanding

• A cannonball is shot with an initial speed of 50
  m/s at a launch angle of 400 toward a castle wall
  220m away. The height of the wall is 30 m. Assume
  that effects due to the air are negligible.
• Show that the cannonball will strike the wall.

We need now only show that the height of the ball
is below 30 m when the horizontal displacement
is 220m
This is less than 30 m, so contact
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Understanding

• A cannonball is shot with an initial speed of 50
  m/s at a launch angle of 400 toward a castle wall
  220m away. The height of the wall is 30 m. Assume
  that effects due to the air are negligible.
• How long will it take for the cannonball to
  strike the wall?

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Understanding

• A cannonball is shot with an initial speed of 50
  m/s at a launch angle of 400 toward a castle wall
  220m away. The height of the wall is 30 m. Assume
  that effects due to the air are negligible.
• At what height above the base of the wall will
  the cannonball strike?

From (a) we have 23 m
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Understanding
A physics student is driving home after class.
The car is travelling at 14.7 m/s when it
approaches an intersection. The student estimates
that he is 20.0 m from the entrance to the
intersection (10.0 m wide) when the traffic light
changes from green to yellow. The light will
change from yellow to red in 3.00 seconds. The
maximum safe deceleration of the car is 4.00 m/s2
while the maximum acceleration of the car is 2.00
m/s2. Should the physics student a) decelerate
and stop or b) accelerate and travel through the
intersection? Note there is a police car
directly behind the student.
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Understanding
A physics student is driving home after class.
The car is travelling at 14.7 m/s when it
approaches an intersection. The student estimates
that he is 20.0 m from the entrance to the
intersection (10.0 m wide) when the traffic light
changes from green to yellow. The light will
change from yellow to red in 3.00 seconds. The
maximum safe deceleration of the car is 4.00 m/s2
while the maximum acceleration of the car is 2.00
m/s2. Should the physics student a) decelerate
and stop or b) accelerate and travel through the
intersection? Note there is a police car
directly behind the student.
Lets try braking first and see how far the car
travels in the 3 seconds.
Data Inventory
We shall use
Therefore the student will travel 6.1 m into the
intersection (not good with police car behind
him)
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Understanding
A physics student is driving home after class.
The car is travelling at 14.7 m/s when it
approaches an intersection. The student estimates
that he is 20.0 m from the entrance to the
intersection (10.0 m wide) when the traffic light
changes from green to yellow. The light will
change from yellow to red in 3.00 seconds. The
maximum safe deceleration of the car is 4.00 m/s2
while the maximum acceleration of the car is 2.00
m/s2. Should the physics student a) decelerate
or b) accelerate and travel through the
intersection? Note there is a police car
directly behind the student.
Now lets try accelerating and see how far the
car travels before the light turns red.
Data Inventory
We shall use
Therefore the student will travel about 23 m past
the intersection before the light turns red.
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Understanding

• A car traveling at a constant speed of 30 m/s
  passes a highway patrol police car which is at
  rest. The police officer accelerates at a
  constant rate of 3.0 m/s2 and maintains this
  rate of acceleration until he pulls next to the
  speeding car. Assume that the police car starts
  to move at the moment the speeder passes the car.
  Determine
• The time required for the police officer to catch
  the speeder?
• The distance travelled during the chase?

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Understanding

• A car traveling at a constant speed of 30 m/s
  passes a highway patrol police car which is at
  rest. The police officer accelerates at a
  constant rate of 3.0 m/s2 and maintains this
  rate of acceleration until he pulls next to the
  speeding car. Assume that the police car starts
  to move at the moment the speeder passes the car.
  Determine
• The time required for the police officer to catch
  the speeder?

Plan of attack If we can find a position
function for both the motorist and the police car
in terms of time, then we can set both functions
equal to each other (same position) and solve for
time
Data Inventory motorist
Data Inventory Police
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Understanding
Lets set then equal and solve
Therefore
or
Therefore the police car catches up with the
speeder at 20s (the 0s is when the car initially
passes the police car)
27
Understanding

• A car traveling at a constant speed of 30 m/s
  passes a highway patrol police car which is at
  rest. The police officer accelerates at a
  constant rate of 3.0 m/s2 and maintains this
  rate of acceleration until he pulls next to the
  speeding car. Assume that the police car starts
  to move at the moment the speeder passes the car.
  Determine
• The distance travelled during the chase?

Since we know the time (20s) from part a), we
need only plug it into the distance formula from
either car. lets use the speeder
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Understanding

• A stone is thrown vertically upward from the edge
  of a building 19.6 m high with an initial
  velocity of 14.7 m/s. The stone just misses the
  building on the way down and strikes the street
  below. Determine
• The time of flight?
• The velocity of the stone just before it strikes
  the ground ?

29
Understanding

• A stone is thrown vertically upward from the edge
  of a building 19.6 m high with an initial
  velocity of 14.7 m/s. The stone just misses the
  building on the way down and strikes the street
  below. Determine
• The time of flight?

Work
Given
Therefore
Flight time is 4 s
Required
Relationship
30
Understanding
A stone is thrown vertically upward from the edge
of a building 19.6 m high with an initial
velocity of 14.7 m/s. The stone just misses the
building on the way down and strikes the street
below. Determine b) The velocity of the stone
just before it strikes the ground ?
Given
Work
Required
The negative value in the velocity indicates that
the stone is travelling downward.
Relationship

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Question 1

• In a carnival booth, you win a stuffed giraffe if
  you toss a quarter into a small dish. The dish is
  on a shelf above the point where the quarter
  leaves your hand and is a horizontal distance
  2.1m from your hand. If the coin is tossed with a
  velocity of 6.4 m/s at an angle of 600 above the
  horizontal, and the coin lands in the dish.
• What is the height of the shelf above the point
  where the coin leaves your hand?
• What is the vertical component of the velocity of
  the coin just before it lands in the dish?

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Solution to Question 1

• In a carnival booth, you win a stuffed giraffe if
  you toss a quarter into a small dish. The dish is
  on a shelf above the point where the quarter
  leaves your hand and is a horizontal distance
  2.1m from your hand. If the coin is tossed with a
  velocity of 6.4 m/s at an angle of 600 above the
  horizontal, and the coin lands in the dish.
• What is the height of the shelf above the point
  where the coin leaves your hand?
• What is the vertical component of the velocity of
  the coin just before it lands in the dish?

Since the horizontal speed is constant, we can
determine how long it took to move horizontally
2.1m
Using this time and having the initial point
taken as height zero, we can now determine the
height at t0.65625s
33
Solution to Question 1

• In a carnival booth, you win a stuffed giraffe if
  you toss a quarter into a small dish. The dish is
  on a shelf above the point where the quarter
  leaves your hand and is a horizontal distance
  2.1m from your hand. If the coin is tossed with a
  velocity of 6.4 m/s at an angle of 600 above the
  horizontal, and the coin lands in the dish.
• What is the height of the shelf above the point
  where the coin leaves your hand?
• What is the vertical component of the velocity of
  the coin just before it lands in the dish?

The negative sign reminds us that the coin is
moving down.
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Question 2

• Mr. Burns does daredevil stunts in his spare
  time. His last stunt was to attempt to jump
  across a river on a motorcycle. The takeoff ramp
  was inclined at 53.00, the river was 40.0 m wide,
  and the bank was 15.0 m lower than the top of the
  ramp. The river was 100m below the ramp.
• What should his speed have been at the top of the
  ramp to have made it to the edge of the far bank?
• If Mr. Burns speed was only half of that in a)
  where did he land?

35
Solution to Question 2

• Mr. Burns does daredevil stunts in his spare
  time. His last stunt was to attempt to jump
  across a river on a motorcycle. The takeoff ramp
  was inclined at 53.00, the river was 40.0 m wide,
  and the bank was 15.0 m lower than the top of the
  ramp. The river was 100m below the ramp.
• What should his speed have been at the top of the
  ramp to have made it to the edge of the far bank?
• If Mr. Burns speed was only half of that in a)
  where did he land?

Now substitute and solve for v
We first need to determine the time it takes to
be 15m below starting point and the time to move
horizontally 40m. Then solve these two
simultaneous equations
Solving the second equation for t
36
Solution to Question 2

• Mr. Burns does daredevil stunts in his spare
  time. His last stunt was to attempt to jump
  across a river on a motorcycle. The takeoff ramp
  was inclined at 53.00, the river was 40.0 m wide,
  and the bank was 15.0 m lower than the top of the
  ramp. The river was 100m below the ramp.
• What should his speed have been at the top of the
  ramp to have made it to the edge of the far bank?
• If Mr. Burns speed was only half of that in a)
  where did he land?

Lets find the time to reach a vertical position
of -100m.
How about his horizontal position at the same time