Exam 4: Motion in Two Dimensions

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 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?

A particle moves at a constant speed in a circular path with a radius of 2.06 cm. If the particle makes four revolutions each second, what is the magnitude of its acceleration?

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

Two balls, projected at different times so they don't collide, have trajectories A and B, as shown below. Which statement is correct?

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 and . 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° with the vertical. Find the speed with which the drops are falling.

A race car moving with a constant speed of 60 m/s completes one lap around a circular track in 50 s. What is the magnitude of the acceleration of the race car?

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

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 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 6400 km. Determine the speed of the satellite, and the time to complete one orbit around the Earth.

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 0.20-km wide river has a uniform flow speed of 3.0 m/s toward the east. A boat with a speed of 8.0 m/s relative to the water leaves the south bank and heads in such a way that it crosses to a point directly north of its departure point. How long does it take the boat to cross the river?

A projectile starts at the coordinate origin, where the displacement vector also originates. The initial velocity, v₀, makes an angle θ₀ with the horizontal where 0 < θ₀ < 90°. At the instant when the projectile is at the highest point of its trajectory, the displacement, velocity and acceleration vectors are , and . Which statement is true?

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:

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(s). -Refer to Exhibit 4-2. The direction of the acceleration, , at point B, is shown by the arrow in

The vector indicates the instantaneous displacement of a projectile from the origin. At the instant when the projectile is at , its velocity and acceleration vectors are and . Which statement is correct?

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 carnival Ferris wheel has a 15-m radius and completes five turns about its horizontal axis every minute. What is the acceleration of a passenger at his lowest point during the ride?