Exam 3: Motion in Two Dimensions

A tennis player wants to slam a serve at O so that the ball lands just inside the opposite corner of the court.What should the ratio $\frac { v _ { 0 y } } { v _ { 0 x } }$ be for the initial velocity $\overrightarrow { \mathbf { v } } _ { 0 }$ ? The time t = 0 is the time when the ball is hit by the racket.

Given the equations below,which description best fits the physical situation? $60.4 \mathrm {~m} = \left( 40.0 \frac { \mathrm { m } } { \mathrm { s } } \right) ( 2.00 \mathrm {~s} ) - \frac { 1 } { 2 } \left( 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } \right) ( 2.00 \mathrm {~s} ) ^ { 2 }$

Which of the following quantities is directly proportional to the time interval after a projectile has left the barrel that shot it out? The x axis is horizontal;the y axis is vertically upward.

A car travels in a due northerly direction at a speed of 55 km/h.The traces of rain on the side windows of the car make an angle of 60 degrees with respect to the horizontal.If the rain is falling vertically with respect to the earth,what is the speed of the rain with respect to the earth?

A tennis player standing 12.6 m from the net hits the ball at 3.00 $\degree$ above the horizontal.To clear the net,the ball must rise at least 0.330 m.If the ball just clears the net at the apex of its trajectory,how fast was the ball moving when it left the racket?

Exhibit 4-2 Newton approximated motion in a circle as a series of linear motions,as in the polygon below. Assume that the particle moves at constant speed v_A from A to B,and at constant speed v_B from B to C. Use this exhibit to answer the following question . -Refer to Exhibit 4-2.The direction of the change in velocity, $\Delta \vec { v }$ ,at point B,is shown by the arrow in

A rock is projected from the edge of the top of a building with an initial velocity of 12.2 m/s at an angle of 53 $\degree$ above the horizontal.The rock strikes the ground a horizontal distance of 25 m from the base of the building.Assume that the ground is level and that the side of the building is vertical.How tall is the building?

Exhibit 4-2 Newton approximated motion in a circle as a series of linear motions,as in the polygon below. Assume that the particle moves at constant speed v_A from A to B,and at constant speed v_B from B to C. Use this exhibit to answer the following question . -Refer to Exhibit 4-2.The direction of the acceleration, $\overrightarrow { \mathbf { a } }$ ,at point B,is shown by the arrow in

A space station of diameter 80 m is turning about its axis at a constant rate.If the acceleration of the outer rim of the station is 2.5 m/s²,what is the period of revolution of the space station?

An airplane flies horizontally with a speed of 300 m/s at an altitude of 400 m.Assume that the ground is level.At what horizontal distance from a target must the pilot release a bomb so as to hit the target?

Two cooks standing side by side in a restaurant pull their beaters out of the dough at the same instant.A glob of dough flies off each beater.Each glob lands on the top of a tin the same horizontal distance away and at its initial height.However,one lands later than the other.The explanation is that they left the beaters at angles $\theta$ ₁ and $\theta$ ₂ such that:

Two cars are traveling around identical circular racetracks.Car A travels at a constant speed of 20 m/s.Car B starts at rest and speeds up with constant tangential acceleration until its speed is 40 m/s.When car B has the same (tangential)velocity as car A,it is always true that:

A particle moves along a circular path having a radius of 2.0 m.At an instant when the speed of the particle is equal to 3.0 m/s and changing at the rate of 5.0 m/s²,what is the magnitude of the total acceleration of the particle?

A particle leaves the origin with a velocity of 7.2 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (3.0 î - 2.0 ĵ)m/s².At the instant the particle moves back across the x axis (y = 0),what is the value of its x coordinate?

At t = 0,a particle leaves the origin with a velocity of 9.0 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (2.0i -4.0j)m/s².At the instant the x coordinate of the particle is 15 m,what is the speed of the particle?

A rock is thrown from the edge of the top of a 100-ft tall building at some unknown angle above the horizontal.The rock strikes the ground a horizontal distance of 160 ft from the base of the building 5.0 s after being thrown.Assume that the ground is level and that the side of the building is vertical.Determine the speed with which the rock was thrown.

With the x axis horizontal and the y axis vertically upward,the change in the horizontal component of velocity, $\Delta$ v_x,and the change in the vertical component of velocity, $\Delta$ v_y,of a projectile are related to the time since leaving the barrel, $\Delta$ t,as

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 $\overrightarrow { \mathbf { r } } = \left( 1.61 \times 10 ^ { 6 } \tilde { \mathbf { i } } + 9.14 \times 10 ^ { 3 } \tilde { \mathbf { j } } \right) \mathrm { m }$ and $\overrightarrow { \mathbf { v } } = + 224 \hat { \mathbf { i } } \frac { \mathrm { m } } { \mathrm { s } }$ . The plane is most likely

A car is driven 1 200 m north at 20.0 m/s and then driven 1 600 m east at 25.0 m/s.What is the magnitude of the average velocity for this trip?

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 $\overrightarrow { \mathbf { r } } = \left( 1.61 \times 10 ^ { 6 } \hat { \mathbf { i } } \right) \mathrm { m }$ and $\overrightarrow { \mathbf { v } } = + 100 \hat { \mathbf { i } } \frac { \mathrm { m } } { \mathrm { s } }$ . The plane is most likely