Exam 3: Vectors and Motion in Two Dimensions

The sum of two vectors of fixed magnitudes has its minimum magnitude when the angle between these vectors is

A ball rolls over the edge of a platform with only a horizontal velocity. The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m. What is the horizontal velocity of the ball just before it touches the ground? Neglect air resistance.

A hockey puck slides off the edge of a horizontal platform with an initial velocity of 28.0 m/shorizontally in a city where the acceleration due to gravity is 9.81 m/s². The puck experiences no significant air resistance as it falls. The height of the platform above the ground is 2.00 m. What is the angle below the horizontal of the velocity of the puck just before it hits the ground?

The Moon is accelerated toward the earth, so it is gradually getting closer to the earth.

A 960-m wide river flows at 16 m/s as shown in the figure. Alice and John have a race in identical boats which each travel 20 m/s in still water. Alice leaves point A and steers so that she goes straight to point B directly across and then back to A. John leaves point A and steers up to point C (960 m upstream)and then returns to A. (a)Which person arrives back at point A first? (b)How much sooner than the loser does the winner arrive back at point A?

A plane has an airspeed of 200 m/s northward, and is in a wind of 50.0 m/s to the west. The plane's speed relative to the ground is

A plane flying horizontally at a speed of 50 m/s and at an elevation of 160 m drops a package, and 2.0 s later it drops a second package. How far apart will the two packages land on the ground if air resistance is negligible?

A boy kicks a football from ground level with an initial velocity of 20 m/s at an angle of 30° above the horizontal. What is the horizontal distance to the point where the football hits the ground if we neglect air resistance?

A ball is thrown at an original speed of 8.0 m/s at an angle of 35° above the horizontal. If there is no air resistance, what is the speed of the ball when it returns to the same horizontal level?

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 $65 \mathrm {~min}$ less than the trip from A to B. What is the airspeed (assumed constant)of the plane relative to the air (that is, the airspeed)?

If a vector $\overrightarrow { \mathrm { A } }$ has components A_x < 0, and A_y > 0, then the angle that this vector makes with the positive x-axis must be in the range

A ball thrown horizontally from a point 24 m above the ground, strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown, assuming negligible air resistance?

Consider two vectors $\overrightarrow { \mathrm { A } }$ and $\overrightarrow { \mathrm { B } }$ shown in the figure. The difference $\overrightarrow { \mathrm { A } }$ - $\overrightarrow { \mathrm { B } }$ is best illustrated by A. B. C. D.

An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the point of origin of the flight. The plane flies with an airspeed of 120 m/s. If a constant wind blows at 10 m/s toward the west during the flight, what direction must the plane fly relative to the air to arrive at the destination?

A point on a wheel of radius 40 cm that is rotating at a constant 5.0 revolutions per second is located 0.20 m from the axis of rotation. What is the acceleration of that point due to the spin of the wheel?

When Jeff ran up a hill at 7.0 m/s, the horizontal component of his velocity vector was 5.1 m/s. What was the vertical component of Jeff's velocity?

Three vectors, $\overrightarrow { \mathrm { S } }$ , $\overrightarrow { \mathbf { T } }$ , and $\overrightarrow { \mathrm { U } }$ , have the components shown in the table. What is the magnitude of the resultant of these three vectors? x component y component 3.50 -4.50 2.00 0.00 -5.50 2.50

A hobbyist launches a projectile from ground level on a horizontal plain. It reaches a maximum height of 72.3 m and lands 111 m from the launch point, with no appreciable air resistance. What was the angle of launch if g = 9.80 m/s²?

A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. What is the speed of the current?

A shell is launched with a velocity of 100 m/s at an angle of 30.0° above horizontal from a point on a cliff 50.0 m above a level plain below. How far from the base of the cliff does the shell strike the ground? There is no appreciable air resistance, and g = 9.80 m/s² at the location of the cliff.