Exam 3: Motion in a Plane

An ant crawls in a straight line at a constant speed of 0.35 m/s, beginning in the corner of a square classroom that is 5.00 m on a side. It first crosses the diagonal of the room and then turns to the right, continuing at 0.45 m/s to the far corner of the same wall from which it began. What was the ant's average speed for the whole trip?

A baseball is struck by a batter at an angle such that it reaches its maximum height at the location of the pitcher-and just grazes the top of the pitcher's head (at an elevation of 1.50 m above the launch point of the baseball). The pitcher is a horizontal distance of 20.0 m from the point at which the ball was struck. What was the launch speed for the baseball?

The velocity of a boat with respect to the water is 4.0 m/s at an angle of 30.0 degrees NORTH of EAST. The velocity of the water with respect to the ground is 3.0 m/s at an angle of 90.0 degrees NORTH of EAST. What is the velocity of the boat with respect to the ground?

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 time it takes for the projectile to hit the ground?

A vector of magnitude 3.8 directed along the positive x-axis combines with a second vector directed along the positive y-axis to produce a total vector of magnitude 6.1. What is the magnitude of the second vector?

A projectile is projected from the origin with a velocity of 20.0 m/s at an angle of 30.0 degrees above the horizontal. The projectile lands on a roof that is 4.00 m high. What is the speed when the projectile hits the roof?

A projectile is launched from the edge of a cliff with a velocity of 15.0 m/s at an angle of 30.0 degrees above the horizontal. Ignoring air resistance, what is the velocity of the projectile 2.00 seconds later?

Given that a vector has components (120 m, −60.0 m), find the magnitude of the vector.

If you add two vectors with magnitudes of 200 and 40, which of the following is a possible resultant magnitude?

Vector A has a magnitude of 3.0 units and makes an angle of −90.0º with the positive x-axis. Vector B has a magnitude of 4.0 units and makes an angle of −120º with the positive x-axis. What is the direction of the vector sum A + B relative to the positive x-axis?

A river flows toward the east at 2.2 m/s. Steve can swim 2.5 m/s in still water. If he wishes to cross the river so that his direction is directly northward, how long will it take him to cross the 75 m wide river?

Given that a vector has components (120 m, −60.0 m), find the direction of the vector relative to the positive x-axis.

An ant travels 30 cm east, 25 cm north, and finally 15 cm west. What is the direction of its displacement with respect to its starting point?

Vector A has a magnitude of 3.0 units and makes an angle of −90.0º with the positive x-axis. Vector B has a magnitude of 4.0 units and makes an angle of −120º with the positive x-axis. What is the magnitude of the vector sum A + B?

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 time it takes the projectile to reach maximum height?

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 velocity and time when the projectile hits the ground?

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 velocity reached in the upward direction?

The velocity of an airplane with respect to the ground is 2.00 × 10² m/s at an angle of 30.0 degrees NORTH of EAST. The velocity of the airplane with respect to the air is 1.50 × 10² m/s at an angle of 60.0 degrees NORTH of EAST. What is the velocity of the air with respect to the ground?

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 range of the projectile?

A projectile is projected from the origin with a velocity of 20.0 m/s at an angle of 30.0 degrees above the horizontal. The projectile lands on a roof that is 4.00 m high. What is the velocity vector when the projectile hits the roof?