Exam 3: Kinematics in Two Dimensions; Vectors

A stone is thrown horizontally with an initial speed of 10 m/s from the edge of a cliff. A stopwatch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.3 s. What is the Height of the cliff if air resistance is negligibly small?

For general projectile motion with no air resistance, the vertical component of a projectile's acceleration

If a vector has components then the angle that this vector makes with the positive x -axis must be in the range

A velocity vector has components 36 m/s westward and 22 m/s northward. What are the magnitude and direction of this vector?

An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of with the vertical. What is the length of the athlete's jump if air resistance is of no significance?

Vector has a magnitude of 6.0 m and points east of south. Vector has a magnitude of 4.0 m and points west of north. The resultant vector is given by

Find the magnitude and direction of the resultant of the three force vectors, shown in the figure. These vectors have the following magnitudes: A=5.0 lb, B=7.9 lb, and C=8.0 lb. Express the direction of the resultant by specifying the angle it makes with the +x -axis, with counterclockwise angles taken to be positive.

A ball is thrown horizontally from the top of a tower at the same instant that a stone is dropped vertically. Which object is traveling faster when it hits the level ground below if neither of them Experiences any air resistance?

The figure shows four vectors, Vectors each have a magnitude of 7.0 cm, and vectors each have a magnitude of 4.0 cm. Find the x and y components of the sum of these four vectors.

An airplane with an airspeed of 120 km/h has a heading of 30° east of north in a wind that is blowing toward the west at 30 km/h. What is the speed of the plane relative to the ground?

You are traveling at 55 mi/h along the +x-axis relative to a straight, level road and pass a car that is traveling at 45 mi/h. The relative velocity of your car to the other car is

A ball is thrown with an initial velocity of 20 m/s at an angle of above the horizontal. If we can neglect air resistance, what is the horizontal component of its instantaneous velocity at the exact Top of its trajectory?

In a room where g = 9.81 m/s², a hockey puck slides off the edge of a platform with an initial velocity of 28.0 m/s horizontally. The height of the platform above the ground is 2.00 m. What is The speed of the puck just before it hits the ground? The air resistance is negligibly small.

The driver of a motorboat that can move at 10 m/s in still water wishes to travel directly across a river in which the current flows at 5.0 m/s. (a) At what angle, measured from the upstream direction, should the driver head the boat? (b) How many minutes will it take to cross the river if it is 1.6 km wide at that point?

The figure shows three vectors, along with their magnitudes. Determine the magnitude and direction of the vector given by

The x and y components of a vector in a horizontal plane are 4.00 m and 3.00 m, respectively. (a) What is the magnitude of this vector? (b) What angle does this vector make with the positive +y-axis.

For general projectile motion with no air resistance, the horizontal component of a projectile's acceleration

A ball rolls over the edge of a platform with a horizontal velocity of magnitude The height of the platform is 1.6 and the horizontal range of the ball from the base of the platform is 20m. What is the magnitude of if air resistance is negligibly small?

Four vectors, are shown in the figure. The sum of these four vectors is a vector having magnitude and direction

A boy kicks a football from ground level with an initial velocity of 20 m/s at an angle of 30° above the horizontal. What is the horizontal distance to the point where the football hits the ground if we Neglect air resistance?