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Vectors and projectiles exercises · Physics Playground

ExercisesPhysics

Vectors and projectiles

19 problems with worked solutions, from Physics and College Physics.

Start with a random one

Learn it first: Vectors: Arrows With Meaning, Projectile Motion

Physics5.1 Vector Addition and Subtraction: Graphical Methods

ExampleAdding Vectors Graphically by Using the Head-to-Tail Method: A Woman Takes a WalkUse the graphical technique for adding vectors to find the total displacement of a person who walks the following three paths (displacements) on a flat field. First, she walks 25 m in a direction 49 ^∘ north of east.…
ExampleSubtracting Vectors Graphically: A Woman Sailing a BoatA woman sailing a boat at night is following directions to a dock. The instructions read to first sail 27.5 m in a direction 66.0 ^∘ north of east from her current location, and then travel 30.0 m in a direction 112…With a figure
ExampleAdding Velocities: A Boat on a RiverA boat attempts to travel straight across a river at a speed of 3.8 m/s. The river current flows at a speed vriver of 6.1 m/s to the right. What is the total velocity and direction of the boat? You can represent each…

Physics5.2 Vector Addition and Subtraction: Analytical Methods

ExampleAdd the vector A to the vector B shown in Figure 5.25, using the steps above. The x-axis is along the east–west direction, and the y-axis is along the north–south directions. A person first walks 53.0 m in a…With a figure

Physics5.3 Projectile Motion

ExampleA Fireworks Projectile Explodes High and Away (part 1)During a fireworks display like the one illustrated in Figure 5.30, a shell is shot into the air with an initial speed of 70.0 m/s at an angle of 75° above the horizontal. The fuse is timed to ignite the shell just…With a figure
ExampleA Fireworks Projectile Explodes High and Away (part 2)
ExampleA Fireworks Projectile Explodes High and Away (part 3)
ExampleCalculating Projectile Motion: Hot Rock ProjectileSuppose a large rock is ejected from a volcano, as illustrated in Figure 5.31, with a speed of 25.0 m/s and at an angle 35° above the horizontal. The rock strikes the side of the volcano at an altitude 20.0 m lower…With a figure

Physics5.4 Inclined Planes

ExampleFinding the Coefficient of Kinetic Friction on an Inclined PlaneA skier, illustrated in Figure 5.35(a), with a mass of 62 kg is sliding down a snowy slope at an angle of 25 degrees. Find the coefficient of kinetic friction for the skier if friction is known to be 45.0 N. Figure…With a figure
ExampleWeight on an Incline, a Two-Dimensional ProblemThe skier’s mass, including equipment, is 60.0 kg. (See Figure 5.36(b).) (a) What is her acceleration if friction is negligible? (b) What is her acceleration if the frictional force is 45.0 N? Figure 5.36 Now use the…With a figure

Physics5.5 Simple Harmonic Motion

ExampleMeasuring Acceleration due to Gravity: The Period of a PendulumWhat is the acceleration due to gravity in a region where a simple pendulum having a length 75.000 cm has a period of 1.7357 s?
ExampleHooke’s Law: How Stiff Are Car Springs?What is the force constant for the suspension system of a car, like that shown in Figure 5.41, that settles 1.20 cm when an 80.0-kg person gets in? Figure 5.41 A car in a parking lot. (exfordy, Flickr)With a figure

College Physics3.2 Vector Addition and Subtraction: Graphical Methods

Example 3.1Adding Vectors Graphically Using the Head-to-Tail Method: A Woman Takes a WalkUse the graphical technique for adding vectors to find the total displacement of a person who walks the following three paths (displacements) on a flat field. First, she walks 25.0 m in a direction 49.0º north of…

College Physics3.3 Vector Addition and Subtraction: Analytical Methods

Example 3.3Adding Vectors Using Analytical MethodsAdd the vector A to the vector B shown in Figure 3.33, using perpendicular components along the x- and y-axes. The x- and y-axes are along the east–west and north–south directions, respectively. Vector A represents…With a figure

College Physics3.4 Projectile Motion

Example 3.4A Fireworks Projectile Explodes High and AwayDuring a fireworks display, a shell is shot into the air with an initial speed of 70.0 m/s at an angle of 75.0º above the horizontal, as illustrated in Figure 3.38. The fuse is timed to ignite the shell just as it…
Example 3.5Calculating Projectile Motion: Hot Rock ProjectileKilauea in Hawaii is the world’s most continuously active volcano. Very active volcanoes characteristically eject red-hot rocks and lava rather than smoke and ash. Suppose a large rock is ejected from the volcano…With a figure

College Physics3.5 Addition of Velocities

Example 3.6Adding Velocities: A Boat on a RiverFigure 3.46 A boat attempts to travel straight across a river at a speed 0.75 m/s. The current in the river, however, flows at a speed of 1.20 m/s to the right. Refer to Figure 3.46, which shows a boat trying to go…With a figure
Example 3.7Calculating Velocity: Wind Velocity Causes an Airplane to DriftCalculate the wind velocity for the situation shown in Figure 3.47. The plane is known to be moving at 45.0 m/s due north relative to the air mass, while its velocity relative to the ground (its total velocity) is…With a figure
Example 3.8Calculating Relative Velocity: An Airline Passenger Drops a CoinAn airline passenger drops a coin while the plane is moving at 260 m/s. What is the velocity of the coin when it strikes the floor 1.50 m below its point of release: (a) Measured relative to the plane? (b) Measured…With a figure