Exam 3: Vectors and Motion in Two Dimensions

What is the maximum distance we can shoot a dart,provided our toy dart gun gives a maximum initial velocity of 2.78 m/s?

What is the minimum number of vectors (none of which have the same magnitude)for which it is theoretically possible that the sum of those vectors can be equal to zero?

Two particles,A and B,are in uniform circular motion about a common center.The acceleration of particle A is 4.7 times that of particle B.Particle B takes 2.4 times as long for a rotation as particle A.The ratio of the radius of the motion of particle A to that of particle B is closest to:

A child is sitting on the outer edge of a merry-go-round that is 18 m in diameter.If the merry-go-round makes 8.3 rev/min,what is the velocity of the child in m/s?

Are projectiles subject to constant acceleration in two dimensions?

A hobby rocket reaches a height of 72.3 m and lands 111 m from the launch point.What was the angle of launch?

If I throw a rock in a lake at 30° or 60° from horizontal,with the same initial speed,it will splash on the same spot.So what is the difference? Should we only consider angles from 0° to 45°?

A grasshopper leaps into the air at a 62 degree angle above the horizontal.At its highest point,the grasshopper's velocity and acceleration are equal to zero.

A cat leaps to catch a bird.If the cat's jump was at 60.0° off the ground and its initial velocity was 2.74 m/s,what is the highest point of its trajectory?

The product of a vector by a scalar is a vector having the same direction of the original vector but a different magnitude.

The magnitude of a vector cannot be smaller than the magnitude of any of its components.

An aircraft performs a maneuver called an aileron roll.During this maneuver,the plane turns like a screw as it maintains a straight flight path,by using its ailerons to set the wings in circular motion.If it takes the plane 35 s to complete the circle and each wing length is 4.6 m,what is the acceleration of the wing tip?

You walk 53 m to the north,then turn 60° to your right and walk another 45 m.Determine the direction of your displacement vector.Express your answer as an angle relative to east.

A projectile is fired at time t = 0.0 s,from point 0 at the edge of a cliff,with initial velocity components of v_ox = 30 m/s and v_oy =300 m/s.The projectile rises,then falls into the sea at point P.The time of flight of the projectile is 75.0 s. In the figure,the horizontal distance D is closest to:

A plane flies directly from city A to city B,which are separated by 2300 mi.From A to B,the plane flies into a 65 mi/h headwind.On the return trip from B to A,the wind velocity is unchanged.The trip from B to A takes 65 min less than the trip from A to B.What is the airspeed (assumed constant)of the plane?

A glider is tugged by an airplane at 81 m/s when it is released.If the original speed was along the horizontal and the glider is now under a constant acceleration of 2.4 m/s² at 1.1° below the horizontal due to air drag,how long will it take to reach the ground 5.7 km below?

An aircraft performs a maneuver called an aileron roll.During this maneuver,the plane turns like a screw as it maintains a straight flight path,by using its ailerons to set the wings in circular motion.Due to structural strength,an airplane can only withstand an acceleration of 6.1 m/s² on its wing tips.If the wing span is 6.0 m,what is the shortest time it can make a full turn when it performs an aileron roll?