South Pasadena · Honors Physics Name______Period___
3 · Projectile Motion
Station 1 · Vectors vs. Scalars
True/False
1. A vector always has magnitude. ____
2. A scalar always has direction. ____
3. Acceleration due to gravity is a scalar quantity. ____
4. The odometer of a car measures a scalar quantity. ____
5. Label the following as either Vector quantities or Scalar quantities.
Treasure map _____ Velocity _____
Your shoe size _____ Speed _____
Your weight _____ Force _____
Acceleration _____ S.S # _____
6. Two vectors have magnitudes V1 = 3.5 km and V2 = 4.0 km. What are the maximum and minimum magnitudes of their vector sum? ______and ______
7. One car travels due east at 50 km/hr and a second car travels north at 50 km/hr. Do these two cars have equal velocities? ______Explain!
South Pasadena · Honors Physics Name______Period___
3 · Projectile Motion
Station 2 · Velocity Vectors
1. Fill in the missing information: Draw a simple vector diagram for the 2 problems below:
Vector 1(km/hr) /Vector 2 (km/hr) / V 1 + V 2
20.0 m/s E / 45.0 m/s W / ?
8.0 m/s So. / 10.0 m/s E / ?
2. Calculate the resultant velocity of Freda Flyer who normally flies at 100 km/h
and then encounters a 10-km/h headwind (wind coming from ahead). ______
3. Calculate Freda Flyer’s speed in a 10-km/h tailwind (wind coming from behind). ______
4. Calculate the resultant velocity of a pair of 100-km/h velocities at right angles ______
to each other.
5. A colorful “Nemo” fish is on display at the Long Beach Aquarium. If it is swimming
at a speed of 1.5 m/s in a certain direction, and then a burst of water current flows at
a right angle to Nemo with a speed of 1.5 m/s, what is the resultant velocity of Nemo? ______
South Pasadena · Honors Physics Name______Period___
3 · Projectile Motion
Station 3 · Components of Vectors
(Draw vector diagrams for the problems below)
1. Draw a vector at a 45º angle, and the draw in the
horizontal and vertical components of the vector.
2. What is the resultant of two vectors, X & Y whose magnitudes ______
are 60 km/hr and 80 km/hr, and the vectors are at right angles
to each other? Sketch the vector diagram.
3. What is the direction (or angle θ) of the resultant in the previous
question? (Show your work below) ______
4. If a 5-unit vector has a vertical component of 3-units, ______
what is its horizontal component?
5. If a 14-unit vector makes an angle of 45º with the horizontal,
what are its horizontal and vertical components?
6. Using the parallelogram method of adding vectors, show the resultant
of the following two vectors.
7. Using the same two vectors above, use the
head-to-tail method to show the resultant.
South Pasadena · Honors Physics Name______Period___
3 · Projectile Motion
Station 4 · Projectile Motion
True/False
1. Projectiles always maintain a constant horizontal velocity (neglecting air resistance). ______
2. Projectiles always experience a constant vertical acceleration of –10 m/s2 (neglecting air resistance). ______
3. The horizontal motion of a projectile depends on its vertical motion. ______
4. Objects dropped from a moving vehicle have the same velocity as the moving vehicle. ______
5. A tiger leaps horizontally from a 7.5 m high rock with a speed of 4.5 m/s.
How far from the base of the rock will she land? ______
6. A diver running at 1.6 m/s dives out horizontally from the edge of a vertical cliff and
reaches the water below 3.0 s later.
a) How high was the cliff? ______
b) How far from its base did the diver hit the water? ______
7. A ball rolls off the edge of the science balcony with a speed of 10.0 m/s.
What is its horizontal speed after 1.0 second in the air? ______
South Pasadena · Honors Physics Name______Period___
3 · Projectile Motion
Station 5 · Upwardly Launched Projectiles
1. A projectile is shot at an angle into the air. Neglecting air resistance, what is its ______
vertical acceleration?
2. What is its horizontal acceleration? ______
3. At what point in its path does a projectile have minimum speed? ______
4. If you are watering your garden with a water hose from some distance, and the water may not
reach the garden, with what angle should you aim the water so as to help you reach the garden? ______
5. If you aim your water hose at an angle of 30º and the water travels a certain horizontal distance,
with what other angle can you aim the hose so that it travels the same horizontal distance? ______
6. A canon is firing a cannonball upward at an angle of 45º and it travels upward for 3.0 seconds
before reaching its highest point. How many meters below a straight line path will the
cannonball be, 2.0 seconds after being fired? ______
7. If a soccer ball is kicked straight up into the air at an initial speed of 30.0 m/s and it is
in the air for 3.0 seconds, while going up and another 3.0 seconds while going down,
what are the speed and velocity at 2.0 seconds and 5.0 seconds?
(Use g = -10 m/s2) vf = vi + gt
Speed at 2.0 s ______Speed at 5.0 s ______
Velocity at 2.0 s ______Velocity at 5.0 s ______
South Pasadena · Honors Physics Name______Period___
3 · Projectile Motion
Station 6 · Class Activities/Experiments
1. A super ball is dropped from the balcony of the science building and it takes
an average time of 1.15 seconds to fall to the ground. What is the height of the
balcony based on this experiment? ______
2. A rubber ball is launched horizontally from the science balcony with
an initial horizontal velocity of 15 m/s. The height of the balcony is
6.0 meters. How far away horizontally does the projectile land? ______
3. Two students are doing the class experiment, “Predicting the Landing Spot of a Projectile”.
They predict the landing spot of the steel ball to be 36.8 cm away from the base of the
lab table. The ball landed into the cup. The velocity they measured for the steel ball
rolling on the table was 87.5 cm/s. Based on this information, what was the height
of the table? ______
OOOOOOO Vx = 87.5 cm/s
?
36.8 cm
South Pasadena · Honors Physics Name______Period___
3 · Projectile Motion
Station 7 · Class Demonstrations
1. If a blow dart is shot thru a blow dart gun and travels 12.0 meters away
and falls a vertical distance of 4.0 centimeters. What was the initial velocity
of the dart in meters/second? ______
2. What is the acceleration of the dart in the horizontal direction? ______
3. What is the acceleration of the dart in the vertical direction? ______
* * * * * * * * * * * * * * * * * * * * * * * * * * * *
4. In the monkey-hunter demonstration done in class, if the monkey did not drop from the
ceiling (tree), and you wanted to hit the monkey with the steel ball, where should you
aim the steel ball?
a) above the monkey b) at the monkey c) below the monkey
5. In the class demonstration using the orange dart gun and dart and metal washer, explain
why the horizontally fired dart reaches the ground in the same time as the metal washer
which is dropped straight down.
South Pasadena · Honors Physics Name______Period___
3 · Projectile Motion “ANSWERS”
Station 1 · Vectors vs. Scalars
True/False
1. A vector always has magnitude. True
2. A scalar always has direction. False
3. Acceleration due to gravity is a scalar quantity. False
4. The odometer of a car measures a scalar quantity. True
5. Label the following as either Vector quantities or Scalar quantities.
Treasure map V Velocity V
Your shoe size S Speed S
Your weight V Force V
Acceleration V S.S # S
6. Two vectors have magnitudes V1 = 3.5 km and V2 = 4.0 km. What are the maximum and minimum magnitudes of their vector sum? 7.5 km and ± 0.5 km
7. One car travels due east at 50 km/hr and a second car travels north at 50 km/hr. Do these two cars have equal velocities? Explain! No they do not because though their speeds are equal, their directions are not, and therefore, their velocities are different.
South Pasadena · Honors Physics Name______Period___
3 · Projectile Motion “ANSWERS”
Station 2 · Velocity Vectors
1. Fill in the missing information: Draw a simple vector diagram for the problems below:
Vector 1(km/hr) /Vector 2 (km/hr) / V 1 + V 2
20.0 m/s E / 45.0 m/s W / 25.0 m/s W
8.0 m/s So. / 10.0 m/s E / 12.8 m/s @ 51.3 ºS.E.
2. Calculate the resultant velocity of Freda Flyer who normally flies at 100 km/h
and then encounters a 10-km/h headwind (wind coming from ahead). 90 km/hr
3. Calculate Freda Flyer’s speed in a 10-km/h tailwind (wind coming from behind). 110 km/hr
4. Calculate the resultant velocity of a pair of 100-km/h velocities at right angles to each other.
141 km/h @ 45 º
5. A colorful “Nemo” fish is on display at the Long Beach Aquarium. If it is swimming
at a speed of 1.5 m/s in a certain direction, and then a burst of water current flows at
a right angle to Nemo with a speed of 1.5 m/s, what is the resultant velocity of Nemo? 2.1 m/s @ 45 º
South Pasadena · Honors Physics Name______Period___
3 · Projectile Motion “ANSWERS”
Station 3 · Components of Vectors
(Draw vector diagrams for the problems below)
1. Draw below a vector at a 45º angle, and the draw in the
horizontal and vertical components of the vector.
2. What is the resultant of two vectors, X & Y whose magnitudes
are 60 km/hr and 80 km/hr, and the vectors are at right angles 100 km/hr @ 53 º
to each other? Sketch the vector diagram.
3. Angle θ between the two vectors, X & Y = inv tan 60/80 or 36.9º
4. If a 5-unit vector has a vertical component of 3-units,
what is its horizontal component? 4-units (3-4-5 right triangle)
5. If a 14-unit vector makes an angle of 45º with the horizontal,
what are its horizontal and vertical components? 9.9-units each
x2 + x2 = (14)2
2x2 = (14)2
x2 = (14)2 /2
x = 9.9 units
South Pasadena · Honors Physics Name______Period___
3 · Projectile Motion “ANSWERS”
Station 4 · Projectile Motion
True/False
1. Projectiles always maintain a constant horizontal velocity (neglecting air resistance). True
2. Projectiles always experience a constant vertical acceleration of –10 m/s2 (neglecting air resistance). True
3. The horizontal motion of a projectile depends on its vertical motion. False
4. Objects dropped from a moving vehicle have the same velocity as the moving vehicle. True
5. A tiger leaps horizontally from a 7.5 m high rock with a speed of 4.5 m/s. How far from
the base of the rock will she land? t = √2d/g = √2 (7.5 m)/9.8 m/s2 = 1.24 s
dx = vxt = 4.5 m/s x 1.24 s = 5.58 or 5.6 m
6. A diver running at 1.6 m/s dives out horizontally from the edge of a vertical cliff and
reaches the water below 3.0 s later.
a) How high was the cliff? h = ½ gt2 = ½ (9.8 m/s2) x (3.0s)2 = 44.1 m
b) How far from its base did the diver hit the water? dx = vxt = 1.6 m/s x 3.0 s = 4.8 m
7. A ball rolls off the edge of the science balcony with a speed of 10.0 m/s.
What is its horizontal speed after 1.0 second in the air? 10.0 m/s
South Pasadena · Honors Physics Name______Period___
3 · Projectile Motion “ANSWERS”
Station 5 · Upwardly Launched Projectiles
1. A projectile is shot at an angle into the air. Neglecting air resistance, what is its
vertical acceleration? - 9.8 m/s2
2. What is its horizontal acceleration? zero
3. At what point in its path does a projectile have minimum speed? At its highest point
4. If you are watering your garden with a water hose from some distance, and the water may not
reach the garden, with what angle should you aim the water so as to help you reach the garden? @ 45 º
5. If you aim your water hose at an angle of 30º and the water travels a certain horizontal distance,
with what other angle can you aim the hose so that it travels the same horizontal distance? @ 60 º
the complement of 30 º
6. A canon is firing a cannonball upward at an angle of 45º and it travels upward for 3.0 seconds
before reaching its highest point. How many meters below a straight line path will the
cannonball be, 2.0 seconds after being fired?
h = ½ gt2 = ½ (9.8 m/s2) x (2.0s)2 = 19.6 m
7. If the soccer ball is kicked straight up into the air at an initial speed of 30.0 m/s and it is in the air for 3.0 seconds, while going up and another 3.0 seconds while going down, what are the speed and velocity at 2.0 seconds and 5.0 seconds?
(Use g = -10 m/s2) vf = vi + gt
Speed at 2.0 s = 10 m/s Speed at 5.0 s 20 m/s
Velocity at 2.0 s 10 m/s Velocity at 5.0 s - 20 m/s
South Pasadena · Honors Physics Name______Period___
3 · Projectile Motion “ANSWERS”
Station 6 · Class Activities/Experiments
1. A super ball is dropped from the balcony of the science building and it takes