Exam 3: Motion in Two Dimensions

A projectile starts at the coordinate origin,where the displacement vector also originates.The initial velocity,v₀,makes an angle $\theta$ ₀ with the horizontal where 0 < $\theta$ ₀ < 90 $\degree$ .At the instant when the projectile is at the highest point of its trajectory,the displacement,velocity and acceleration vectors are $\overrightarrow { \mathbf { r } }$ , $\overrightarrow { \mathbf { v } }$ and $\overrightarrow { \mathbf { a } }$ .Which statement is true?

A hunter wishes to cross a river that is 1.5 km wide and flows with a velocity of 5.0 km/h parallel to its banks.The hunter uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water.What is the minimum time for crossing?

In a location where the train tracks run parallel to a road,a high speed train traveling at 60 m/s passes a car traveling at 30 m/s in the opposite direction.How long does it take for the train to be 180 m away from the car?

A particle moves in the xy plane in a circle centered on the origin.At a certain instant the velocity and acceleration of the particle are 4.0 ĵ m/s and (-3.0 î- 2.0 ĵ )m/s².What are the x and y coordinates of the particle at this moment?

A particle starts from the origin at t = 0 with a velocity of (16 i? -12 j? )m/s and moves in the xy plane with a constant acceleration of $\overrightarrow { \mathbf { a } }$ = (3.0 i? - 6.0 j? ) m/s². What is the speed of the particle at t = 2.0 s?

A rifle is aimed horizontally at the center of a large target 60 m away.The initial speed of the bullet is 240 m/s.What is the distance from the center of the target to the point where the bullet strikes the target?

A car travels in an oval path as shown below. $\overrightarrow { \mathbf { v } } _ { A }$ = 25 m/s,West,and $\overrightarrow { \mathbf { v } } _ { B }$ = 20 m/s,North.The ratio of the magnitude of the centripetal acceleration at B to that at A, $\frac { a _ { \mathrm { B } } } { a _ { \mathrm { A } } }$ ,is:

Given the equations below,which description best fits the physical situation? $- 99.6 \mathrm {~m} = \left( - 40.0 \frac { \mathrm { m } } { \mathrm { s } } \right) ( 2.00 \mathrm {~s} ) - \frac { 1 } { 2 } \left( 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } \right) ( 2.00 \mathrm {~s} ) ^ { 2 }$

Jane plans to fly from Binghampton,New York,to Springfield,Massachusetts,about 280 km due east of Binghampton.She heads due east at 280 km/h for one hour but finds herself at Keene,which is 294 km from Binghampton in a direction 17.8 degrees north of due east.What was the wind velocity?

The vector $\overrightarrow { \mathbf { r } }$ indicates the instantaneous displacement of a projectile from the origin.At the instant when the projectile is at $\overrightarrow { \mathbf { r } }$ ,its velocity and acceleration vectors are $\overrightarrow { \mathbf { v } }$ and $\overrightarrow { \mathbf { a } }$ .Which statement is correct?

A block is supported on a compressed spring,which projects the block straight up in the air at velocity $\overrightarrow { \mathbf { v } } = v _ { 0 y } \hat { \mathbf { j } }$ .The spring and ledge it sits on then retract.You can win a prize by hitting the block with a ball.When should you throw the ball and in what direction to be sure the ball hits the block? (Assume the ball can reach the block before the block reaches the ground and that the ball is thrown from a height equal to the release position of the block. )

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by $\overrightarrow { \mathbf { r } } = \left( 1.61 \times 10 ^ { 6 } \hat { \mathbf { i } } + 3.00 \times 10 ^ { 3 } \tilde { \mathbf { j } } \right) \mathrm { m }$ and $\overrightarrow { \mathbf { v } } = + ( 150 \hat { \mathbf { i } } - 21 \hat { \mathbf { j } } ) \frac { \mathrm { m } } { \mathrm { s } }$ . The plane is most likely

Raindrops are falling straight downward.When observed from a car traveling at 55.0 mi/h,the drops streak the side window at an angle of 60.0 $\degree$ with the vertical.Find the speed with which the drops are falling.

The speed of a particle moving in a circle 2.0 m in radius increases at the constant rate of 4.4 m/s².At an instant when the magnitude of the total acceleration is 6.0 m/s²,what is the speed of the particle?

A motorcycle daredevil wants to ride up a 50.0 m ramp set at a 30.0 $\degree$ incline to the ground.It will launch him in the air and he wants to come down so he just misses the last of a number of 1.00 m diameter barrels.If the speed at the instant when he leaves the ramp is 60.0 m/s,how many barrels can be used?

While the gondola is rising at a speed of 2.0 m/s,a passenger in a balloon-supported gondola throws a small ball down at a speed of 5.0 m/s relative to his body.A person who measures the ball's velocity at the instant of release will find that the ball's velocity relative to the ground at that instant is

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by $\overrightarrow { \mathbf { r } } = \left( 1.61 \times 10 ^ { 4 } \hat { \mathbf { i } } + 9.00 \times 10 ^ { 3 } \hat { \mathbf { j } } \right) \mathrm { m }$ and $\overrightarrow { \mathbf { v } } = ( 150 \hat { \mathbf { i } } - 21 \hat { \mathbf { j } } ) \frac { \mathrm { m } } { \mathrm { s } }$ . The magnitude,in meters,of the plane's displacement from the origin is

A car travels in a flat circle of radius R.At a certain instant the velocity of the car is 24 m/s west,and the total acceleration of the car is 2.5 m/s² 53 $\degree$ north of west.Which of the following is correct?

Exhibit 4-1 While her kid brother is on a wooden horse at the edge of a merry-go-round,Sheila rides her bicycle parallel to its edge.The wooden horses have a tangential speed of 6 m/s.Sheila rides at 4 m/s.The radius of the merry-go-round is 8 m. Use this exhibit to answer the following question . -Refer to Exhibit 4-1.At what time intervals does Sheila encounter her brother,if she rides in the direction of rotation of the merry-go-round?

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?