Exam 3: Vectors and Two-Dimensional Motion

A helicopter is traveling at 40 m/s at a constant altitude of 100 m over a level field.If a wheel falls off the helicopter,with what speed will it hit the ground? (g = 9.8 m/s² and air resistance negligible)

A particle moves east at constant velocity for a time interval DT.It then moves north at a constant velocity,with the same speed as before,for another time interval DT.Finally it moves east again with the original velocity.At the instant an additional time interval DT has elapsed,which of the following are true about the average velocity and the average acceleration for the motion described?

A boat moves at 10.0 m/s relative to the water.If the boat is in a river where the current is 2.00 m/s,how long does it take the boat to make a complete round trip of 1 000 m upstream followed by a 1 000-m trip downstream?

A taxicab moves five blocks due north,five blocks due east,and another two blocks due north.Assume all blocks are of equal size.What is the magnitude of the taxi's displacement,start to finish?

Four vectors all have the same magnitude.Vector 1 is at 30 $\degree$ ,Vector 2 is at 135 $\degree$ ,vector 3 is at 240 $\degree$ ,and Vector 4 is at 315 $\degree$ .Which vector has the greatest magnitude x-component and which vector has the greatest magnitude y-component?

A projectile is launched at an angle q above the horizontal.Three seconds later the projectile is moving the same angle q below the horizontal.Which of the following (actual values with units,not just algebraic symbols)can be found from the information given?

A track star in the broad jump goes into the jump at 12 m/s and launches himself at 20 $\degree$ above the horizontal.How long is he in the air before returning to Earth? (g = 9.8 m/s²)

Vector is 3 m long,and vector is 4 m long.The length of the sum of the vectors must be:

A hiker walks 200 m west and then walks 100 m north.In what direction is her resulting displacement?

Vectors , ,and have magnitudes 6,11,and 20.When these vectors are added,what is the least possible magnitude of their resultant?

In a 2-dimensional Cartesian system,the x-component of a vector is known,and the angle between vector and x-axis is known.Which operation is used to calculate the magnitude of the vector? (taken with respect to the x-component)

A rifle is aimed horizontally toward the center of a target 100 m away.If the bullet strikes 10 cm below the center,what was the velocity of the bullet? (Ignore air friction. )

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.4 m/s at an initial angle of 30.0 $\degree$ with respect to the horizontal.What is the maximum vertical displacement that the ball reaches during its trajectory?

Jack pulls a sled across a level field by exerting a force of 110 N at an angle of 30 $\degree$ with the ground.What are the parallel and perpendicular components,respectively,of this force with respect to the ground?

A baseball leaves the bat with a speed of 44.0 m/s and an angle of 30.0 $\degree$ above the horizontal.A 5.0-m-high fence is located at a horizontal distance of 132 m from the point where the ball is struck.Assuming the ball leaves the bat 1.0 m above ground level,by how much does the ball clear the fence?

A jet airliner moving at 500 mph due east moves into a region where the wind is blowing at 120 mph in a direction 30.0 $\degree$ north of east.What is the new velocity and direction of the aircraft?

A projectile is fired directly upwards at 49.0 m/s.A second projectile is dropped from rest at some higher elevation at the instant the first projectile is fired and passes the first projectile 3.00 s later.From the frame of reference of the first projectile,what is the velocity of the second projectile as it passes by?

A stone is thrown with an initial speed of 15 m/s at an angle of 53 $\degree$ above the horizontal from the top of a 35 m building.If g = 9.8 m/s² and air resistance is negligible,then what is the magnitude of the horizontal component of velocity as the rock strikes the ground?

A baseball is thrown by the center fielder (from shoulder level)to home plate where it is caught (on the fly at shoulder level)by the catcher.At what point is the magnitude of the acceleration at a minimum? (air resistance is negligible)

Superguy is flying at treetop level near Paris when he sees the Eiffel Tower elevator start to fall (the cable snapped).His x-ray vision tells him Lois LaTour is inside.If Superguy is 1.00 km away from the tower,and the elevator falls from a height of 240 m,how long does Superguy have to save Lois,and what must be his average speed?