Vectors, Kinematics, Dynamics

Vectors, Kinematics, Dynamics Quiz

Multiple Choice Problems

• Calculation of A - 2B + 3C, where A=(-1 + 2.5j + 5.0k), B=(3.0î – 7.0j + 4.0k), and C=(î + j - k), results in (-4.0î + 19.5j – 6k)
• A vector B in the 1st quadrant of the xy-plane with magnitude 9.00, making a 30.0° angle with the +y-axis, results in A × B being 74.3 k units, given A = 13.0î + 6.0j
• The angle between vectors A and B is approximately 35.2 degrees.
• Average velocity is none of the above, since there is no displacement and thus no average velocity.

Cargo Ship Problem

• A cargo ship travels 2221 nautical miles from Manila to Thailand in 8.3 days, results in the average velocity being of 5.7 m/s.

Particle Motion Problem

• When a particle begins moving in the -y direction from rest and comes to a stop, its acceleration is negative while beginning to move, and more positive when coming to a stop

Caterpillar Problem

• A caterpillar escapes a predator with a velocity function of 0.50t + 0.75t^2.
• The caterpillar's average acceleration from t=0s to t=0.8 s is 0.24 in/s².

Throckmorton and Dog Problem

• Throckmorton is 5.00 meters ahead of a dog.
• The dog reaches a velocity of 7.00 m/s, which results in the time to catch up is 1.43 s.

Ball Thrown Upwards Problem

• A ball thrown upwards (+y direction) experiences the following velocity sequence: decreasing, 0, then increasing.

Ball Thrown Upwards in +y Direction Problem

• A ball thrown straight upward returns to the thrower's hand in 4.00 seconds.
• The initial velocity is 19.6 m/s.

Projectile Motion Statement

• The false statement about projectile motion is: "The greater the launch angle, the farther its horizontal range."

Shuttlecock Problem

• A shuttlecock launched at 5.5 m/s at a 35° angle has a horizontal range of approximately 2.9 m, when air resistance is negligible

Kitchen Cart Problem

• A kitchen staff pushes a cart on a frictionless horizontal surface.
• The cart moves an additional 46.6m in the next 6.00s.

Coin on Rotating Disc

• A coin on a rotating disc with a 0.40 m radius revolves at 60.0 rev/min when 0.190 m from the axis
• The static friction coefficient between the coin and disc is 0.76.

Blocks on Inclined Plane Problem

• A block of mass m1 rests on a frictionless inclined plane at angle θ.
• The condition for m1 to slide down is when m2g > m1gsinθ.

Highway Curve Problem

• A highway curve with a 123 m radius should be banked at 27.0° for vehicles at 55.4 mi/h to safely round it.

Box in Car Problem

• A 6.0-kg box has static and kinetic friction coefficients of 0.18 and 0.13.
• Time before the box hits the rear is 1.4 s.

Projectile Launched from Building

• The time of flight of the projectile is proportional to sqrt(Rearth + h) / sqrt(Rearth)) times higher

Astronaut in Space Station Problem

• An 81-kg astronaut experiences artificial gravity in a rotating space station, with a centripetal acceleration of 2.0 m/s².
• The scale reads 792 N.

Satellite around Mars Problem

• A satellite orbits Mars at 600 km altitude, given Mars' mass (6.39×10^23 kg) and radius (3.39×10^6 m) from the center.
• The satellite's period is 1.67 hours.