Physics 20 - STA
Work Booklet
Unit I – Kinematics
Chapter 2 – Kinematics in Two-Dimensions
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Physics 20 Unit 1: Kinematics
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2.1 –Vectors: One and Two Dimensional
1. A bouncy ball dropped from a height of 10.0 m bounces back 8.0 m, then drops and rebounds
4.0 m, and finally 2.0 m. Find the distance the ball travels and its displacement from the drop
point.
2. Solve for the unknown in each of the following right triangles.
3. Tracy walks the following route from the rotunda in her school: 20 m due south and then 30 m
east through the cafeteria to her physics class. Determine the displacement of the physics class
relative to the rotunda.
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4. A train travels due east for a distance of 120 km at a speed of 100 km/h. It then turns south and
travels 230 km at 120 km/h. Calculate the trains
a) displacement relative to its starting point.
b) average velocity.
5. During the final play of a football game the home team needs 6 yards to score a touchdown
and win. The ball is thrown to the running back who catches it on the line of scrimmage and runs
9 yards 40o E of N as represented by the arrow in the diagram. Does he cross the goal line?
Answers
1) 36.0 m, 8.0 m down; 2) a) 6.4 m, b) 5.3 cm, c) 2.9 mm, d) 31o, e) 44o, f) 25o
b). 83.2 km/h, 62.4o S of E 5) yes
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3) 36 m, 56o E of S 4.a) 259 km, 62.4o S of E,
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2.2 Two-Dimensional Vector Addition
1. A physics student walks 10 m east from her locker to the cafeteria and then walks 20 m at
30o S of E to the food counter. Determine her displacement relative to her locker.
2. A horse trots 80.0 m due west, stops at a watering hole for a drink, and then gallops 120 m at
40.0o S of W. Find the displacement of the horse.
3. Calvin walks 3.0 km to the north and then, from that point, turns and walks 5.0 km at 50o S
of E. Determine his displacement relative to his starting position.
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4. A hiker in the mountains uses her compass to navigate. She hikes north for 6.0 km, then
turns and hikes at 60o E of N for 4.0 km. She takes a lunch break, then hikes for 8.0 km at
30o S of E. Finally, she hikes 5.0 km at 30o S of W, and discovers she is totally lost.
Determine the hiker’s displacement relative to her starting point.
5. A jogger runs with a velocity of 6.0 km/h [25° N of W] for 35 min and then changes direction,
jogging for 20 min at 4.5 km/h [65° E of N]. Using a vector diagram, determine the jogger’s:
a) total displacement for the workout
b) average velocity for the workout.
Answers
1) 29 m at 20o S of E 2) 188 m at 24.2o S of W
W b) 3.0 km/h, 49o N of W
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3) 3.3 km at 14o S of E
4) 6.2 km at 14o N of E
5) a) 2.8 km, 49o N of
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2.3 Relative Motion and Navigation
1. Clive is rowing his boat across Hickie River. The river is flowing north at 5.30 m/s, and
Clive is rowing east at 2.70 m/s. The river is 30.0 m wide.
a. What is the resultant velocity of Clive in his boat?
b. How long does it take for Clive to get across the river?
2. A rookie Springbank pilot heads north with an air velocity of 120 km/h. He does not
account for the wind blowing at 80 km/h 32o S of W. What is the resultant ground
velocity of his plane?
3. A search and rescue worker knows that a pilot had lost his instruments at night. The pilot
had headed west at 170 km/h, but the wind had been blowing at 90.0 km/h 30.0o N of E.
What would the search and rescue worker use as an estimated ground velocity in finding
the plane?
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4. A river that is flowing due west is crossed by a boat travelling from the south bank to the north
bank. The boat can travel at 30 m/s in still water and the river is moving at 10 m/s.
a) Identify the vector diagram below (A or B) that represents the boat travelling
i) directly across the river
ii) downstream as it crosses the river
b) Determine the resultant velocity for the boat when it is travelling
i) directly across the river
ii) downstream as it crosses the river
c) Determine the direction the boat must point to travel directly across.
5. A small plane can travel with a speed of 265 km/h with respect to the air. If the plane
heads north, deremine its resultant velocity if it encounters
a. A 32.0 km/h headwind
b. A 32.0 km/h tailwind
c. a 32.0 km/h [W] crosswind
Answers
1) a) 5.95 m/s at 27.0o E of N, b) 11.1 s 2) 1.0 x 102 km/h at 49o N of W 3) 102 km/h at 26.0o N of W 4) a) i) A ii) B, b) i)
28 m/s, N ii) 32 m/s, 18o W of N, c) 19o E of N 5) a) 233 km/h [N], b) 297 km/h [N], c) 267 km/h [83.1o N of W]
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2.4 Projectile Motion
1. A car is crash-tested by driving it off a level platform 10.0 m high at 20 m/s. Calculate
the:
a. Time the car takes to hit the ground
b. Distance the car lands from the base of the cliff
2. Participants in a road race take water from a refreshment station and throw their empty
cups away farther down the course. If a runner has a forward speed of 6.20 m/s, how far
in advance of a garbage pail should he release his water cup if the vertical distance
between the lid of the garbage can and the runner’s point of release is 0.50 m?
3. A paintball is fired horizontally from the window of a fort 4.7 m above the ground. It
contacts the ground 20.1 m away and splatters. Determine the paintball’s speed as it
exited the paintball gun. Hint – the paintball is red.
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4. An object is thrown horizontally at a velocity of 18.0 m/s from the top of a cliff. If the
object hit the ground 100.0 m from the base of the cliff, how high is the cliff?
5. A baseball is thrown with a velocity of 27.0 m/s [35o]. How high and how far will it
travel?
6. At the 2004 Olympic Games in Athens, Dwight Phillips won the gold medal in men’s
long jump with a jump of 8.59 m. If the angle of his jump was 23o, what was his takeoff
speed?
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7. A projectile is fired with an initial speed of 120 m/s at an angle of 55.0_ above the
horizontal from the top of a cliff 50.0 m high. Find:
(a) the time taken to reach maximum height
(b) the maximum height
(c) the total time in the air
(d) the range
(e) the components of the final velocity just before the projectile hits the ground
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8. How long will a soccer ball remain in flight if it is kicked with an initial velocity of 25.0
m/s [35.0o]? How far down the field will the ball travel and what will be its maximum
height?
9. A batsman in a cricket game hits a ball at ground level causing the ball to travel upwards
at 30o with an initial speed of 18 m/s. Determine the horizontal distance the ball travels
through the air if it contacts the ground after being missed by a fielder.
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10. A projectile is thrown upwards and comes down to its original level in a parabolic
trajectory. Identify the graphs that would represent the
a. Horizontal components of the projectile’s motion
b. Vertical components of the projectile’s motion
Answers
1) a) 1.43s, b) 29 m
2) 2.0 m
3) 21 m/s
4) 151 m
5) 12.2 m up, out 69.8m 6) 10.8 m/s 7) a) 10.0 s, b)542 m,
8) 2.92 s, dist. = 59.9 m, max. height = 10.5 m 9) 29 m
c) 20.5 s, d) 1.41. km, e) horiz. = 68.8 m/s, vert = -103 m/s
10) a) i, v, iii, b) vii, viii, vi
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