Exam 3: Motion in a Plane

A model airplane is flying north at 12.5 m/s initially, and 25 seconds later is observed heading 30 degrees west of north at 25 m/s. What is the magnitude of the average acceleration during this time interval?

An airplane flying horizontally at a speed of 50.0 m/s and an elevation of 160 m drops a package. Two seconds later it drops a second package. How far apart will the two packages land?

A river flows toward the east at 1.5 m/s. Steve can swim 2.2 m/s in still water. If he wishes to cross the river so that his direction is exactly northward, what direction relative to the water must he swim?

A projectile is projected from the origin with a velocity of 45.0 m/s at an angle of 30.0 degrees above the horizontal. What is the velocity when the projectile hits the ground?

A river flows toward the east at 1.7 m/s. Steve can swim 2.0 m/s in still water. If he swims relative to the water at a direction of 33 degrees west of north, how long will it take him to cross the 75 m wide river?

A displacement vector of magnitude 15.2 km directed along the positive x-axis combines with a second vector to produce a total displacement of magnitude 17.9 km. What is the magnitude of the second vector?

A stone thrown horizontally from a cliff with an initial speed of 10 m/s hits the bottom of the cliff in 4.3 s. What is the height of the cliff?

A rocket is launched from the origin with an acceleration of 20.0 m/s² at an angle of 30.0 degrees above the horizontal. The launch acceleration lasts for 2.00 seconds at which time the fuel is exhausted. The rocket then falls with an acceleration of 9.80 m/s² downward. What is the time it takes to reach maximum height?

A rocket is launched from the origin with an acceleration of 20.0 m/s² at an angle of 30.0 degrees above the horizontal. The launch acceleration lasts for 2.00 seconds at which time the fuel is exhausted. The rocket then falls with an acceleration of 9.80 m/s² downward. What is the maximum height attained?

A projectile is projected from the origin with a velocity of 30.0 m/s at an angle of 45.0 degrees above the horizontal. What is the range of the projectile?

A projectile is projected from the origin with a velocity of 30.0 m/s at an angle of 40.0 degrees above the horizontal. What is the position vector when the projectile is at the maximum height?

The interstate on-ramp is 5.5 km west of your home, and on leaving for grandmother's house you are only able to accomplish an average velocity of 38 km/hr between your home and the on-ramp. At the on-ramp, you wait for traffic for 2.0 min before proceeding toward grandmother's house. If you wish to arrive there, which is 15 km south of the on-ramp, over a river and through some woods, having achieved an average velocity of 42 km/hr for the whole trip, how fast do you need to drive south on the interstate highway?

An ant crawls in a straight line at a constant speed of 0.24 m/s for a distance of 3.0 m, beginning in the corner of a square classroom. It then turns exactly 90 degrees to the right, and proceeds an additional 4.0 m, reaching the far corner of the same wall from which it began. If the second leg of the journey was crawled in half the amount of time as the first, what was the ant's average speed for the whole trip?

A displacement vector D is given as 40.0 m at an angle of 60.0 degrees NORTH of EAST. The D_x component and the D_y component of the vector are

A rocket is launched from the origin with an acceleration of 20.0 m/s² at an angle of 30.0 degrees above the horizontal. The launch acceleration lasts for 2.00 seconds at which time the fuel is exhausted. The rocket then falls with an acceleration of 9.80 m/s² downward. What is the total horizontal distance (range) covered when the rocket hits the ground?

Given that a vector extends from the origin to (−5.0 cm, 8.0 cm), find the magnitude of the vector.

A ball thrown into the air follows a parabolic trajectory. At the highest point in the trajectory

The velocity of a boat with respect to the water is 4.0 m/s at an angle of 30.0 degrees NORTH of WEST. The velocity of the water with respect to the ground is 8.0 m/s at an angle of 45 degrees SOUTH of EAST. What is the velocity of the boat with respect to the ground?

A blue ball is dropped from the roof of a tall building simultaneously with the horizontal launch of a red ball. Ignoring air resistance, which statement is true?

Given that a vector extends from the origin to (−5.0 cm, 8.0 cm), find the direction of the vector relative to the positive x-axis.