Vectors And Motion In Two Dimensions

A velocity vector has a magnitude of 50.0 m/s and is directed at 37° above the positive x-axis. What is the y-component of this velocity?

A displacement vector has components dₓ = −8.0 m and dᵧ = 6.0 m. What is the magnitude of this displacement?

A projectile is launched at 30.0 m/s at an angle of 45° above the horizontal from level ground. At the highest point of its trajectory, which statement correctly describes the projectile’s velocity and acceleration? Use g = 10 m/s².

Vector F⃗₁ has magnitude 12.0 N at 0° (along the positive x-axis) and vector F⃗₂ has magnitude 16.0 N at 90° (along the positive y-axis). What is the direction of the resultant force, measured from the positive x-axis?

A ball is thrown horizontally at 20.0 m/s from the top of a 45.0 m tall building. How far from the base of the building does the ball land? Use g = 10 m/s².

An engineer must aim a sensor so that its 100.0 N detection beam has exactly 50.0 N of force along the horizontal axis. At what angle above the horizontal should the sensor be tilted?

A pilot flies a plane 500 km on a heading 40° north of east, then 300 km due south. What is the resultant x-component (east-west) of the total displacement?

A particle has initial velocity components v₀ₓ = 6.0 m/s and v₀ᵧ = 8.0 m/s and experiences accelerations aₓ = 0 and aᵧ = −10 m/s². What is the speed of the particle at t = 1.0 s?

A rescue package is dropped from a helicopter moving horizontally at 25.0 m/s at an altitude of 125 m. How long does the package take to reach the ground? Use g = 10 m/s².

A football is kicked at 25.0 m/s at 53° above the horizontal from level ground. What is the maximum height reached by the ball? Use g = 10 m/s².

Two displacement vectors each have magnitude 15.0 m. Vector A⃗ points at 0° and vector B⃗ points at 90°. What is the magnitude of their resultant?

A spacecraft in deep space fires two perpendicular thrusters simultaneously. Thruster X provides an acceleration of 3.0 m/s² in the x-direction, and thruster Y provides 4.0 m/s² in the y-direction. Starting from rest, what is the spacecraft’s speed after 10.0 s?

During a soccer match, a ball is kicked with a speed of 18.0 m/s at an angle of 30° above the ground. A second ball is kicked simultaneously with the same speed at 60° above the ground from the same point. Both land at ground level. Which ball has the greater horizontal range?

A stone is launched at 40.0 m/s at 30° above the horizontal from level ground. What is the total time of flight? Use g = 10 m/s².

A cannon fires a shell at 100 m/s at 53° above the horizontal. At t = 2.0 s after launch, what is the angle of the shell’s velocity vector relative to the horizontal? Use g = 10 m/s².

A river flows east at 3.0 m/s. A swimmer aims directly north across the river and swims at 4.0 m/s relative to the water. What is the swimmer’s resultant speed relative to the ground, and in what direction does she actually travel?

A ball is launched vertically upward at 20.0 m/s from a cart moving horizontally at a constant 5.0 m/s. An observer on the ground watches the ball. Which description best characterizes the ball’s path as seen by the ground observer?

If a projectile’s launch speed is doubled while the launch angle and g remain the same, by what factor does the maximum height change?