Exam 3: Motion in Two Dimensions

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

A student in the front of a school bus tosses a ball to another student in the back of the bus while the bus is moving forward at constant velocity.The speed of the ball as seen by a stationary observer in the street:

A fast duck is flying $( 20 \tilde { \mathbf { i } } + 40 \tilde { \mathbf { j } } )$ mi/h at the same altitude as a slow airplane flying with a velocity of $( - 80 \hat { \mathbf { i } } + 40 \tilde { \mathbf { j } } )$ mi/h.How fast and in what direction is the duck moving relative to the airplane?

A car travels in a flat circle of radius R.At a certain instant the velocity of the car is 20 m/s north,and the total acceleration of the car is 2.5 m/s² 37 $\degree$ south of west.Which of the following is correct?

A 0.14-km wide river flows with a uniform speed of 4.0 m/s toward the east.It takes 20 s for a boat to cross the river to a point directly north of its departure point on the south bank.What is the speed of the boat relative to the water?

A stunt pilot performs a circular dive of radius 800 m.At the bottom of the dive (point B in the figure)the pilot has a speed of 200 m/s which at that instant is increasing at a rate of 20 m/s².What acceleration does the pilot have at point B?

A baseball is hit at ground level.The ball is observed to reach its maximum height above ground level 3.0 s after being hit.And 2.5 s after reaching this maximum height,the ball is observed to barely clear a fence that is 97.5 m from where it was hit.How high is the fence?

A football is thrown upward at a 30.0 $\degree$ angle to the horizontal.To throw a 40.0-m pass,what must be the initial speed of the ball?

A car travels around an oval racetrack at constant speed.The car is accelerating

A satellite is in a circular orbit 600 km above the Earth's surface.The acceleration of gravity is 8.21 m/s² at this altitude.The radius of the Earth is 6 400 km.Determine the speed of the satellite,and the time to complete one orbit around the Earth.

The position of an object is given by $\overrightarrow { \mathbf { r } } = \left( - 4.00 t \hat { \mathbf { i } } + 6.00 t ^ { 3 } \hat { \mathbf { j } } \right) \mathrm { m }$ where t is in seconds.At t = 2.0 s,what is the magnitude of the particle's acceleration?

An object moving at a constant speed requires 6.0 s to go once around a circle with a diameter of 4.0 m.What is the magnitude of the instantaneous acceleration of the particle during this time?

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 6.0 î m/s and (3.0 î + 4.0 ĵ1 )m/s².What are the x and y coordinates of the particle at this moment?

A boat moves at 10.0 m/s relative to the water.If the boat is in a river where the current is 2.0 m/s,how long does it take the boat to make a complete round trip of 1.00 km upstream followed by a 1.00 km trip downstream?

Car A leaves point O at t = 0 and travels a quarter circle counterclockwise at 30.0 m/s to point P.Car B will leave point O and travel to point P at the same speed but in a straight line.The radius of the circle is 100 m.At what time should car B leave point O in order to arrive at point P at the same time as car A?

A rifle is aimed horizontally toward the center of a target 0.10 km away,but the bullet strikes 10 cm below the center.Calculate the velocity of the bullet just as it emerges from the rifle.

A particle moves in the xy plane with a constant acceleration given by $\overrightarrow { \mathbf { a } } = - 4.0 \hat { \mathbf { j } } \mathrm { m } / \mathrm { s } ^ { 2 }$ .At t = 0,its position and velocity are 10 i? and $( - 2.0 \tilde { \mathbf { i } } + 8.0 \tilde { \mathbf { j } } ) \mathrm { m } / \mathrm { s }$ ,respectively.What is the distance from the origin to the particle at t = 2.0 s?

A small dense object is suspended from the rear view mirror in a car by a lightweight fiber.As the car is accelerating at 1.90 m/s²,what angle does the string make with the vertical?

A car travels counterclockwise around a flat circle of radius 0.25 km at a constant speed of 20 m/s.When the car is at point A as shown in the figure,what is the car's acceleration?

At t = 0,a particle leaves the origin with a velocity of 5.0 m/s in the positive y direction.Its acceleration is given by $\overrightarrow { \mathbf { a } }$ = (3.0 i? - 2.0j?)m/s².At the instant the particle reaches its maximum y coordinate how far is the particle from the origin?