Unit Vectors Practice Problems

In a two-dimensional coordinate system, any vector can be broken into x -component, and y -components. Determine the x and y components of vector A shown in the figure below. Find the components in terms of the given angle θ.

A baseball pitcher throws the ball, and the batter strikes it for a home run. Determine the angle at which the bat is tilted above the horizontal. The ball's velocity at the instant it leaves the bat is v = (15î + 25ĵ) m/s.

Acceleration (a) is the rate of change in velocity (v) over time (a = dv/dt ). The expression for the subatomic particle's position is given as a function of time r = (5.0î + 4.0ĵ)t² m. Determine the particle's velocity at i) t = 0s and ii) 2s.

Displacement (d) is directly proportional to the velocity (v) and inversely proportional to time (t) (v = d/t). Assume that the particle's initial position is at the origin and that its final position changes over time. Its final position is given as r = (4î + 2.0ĵ)t² m, where t is in seconds. Write an equation that shows the velocity of the particle as a function of time.

An object starts from the origin; determine how the position of the object varies with time at (i) t = 3s and (ii) t = 8s. Its position changes over time according to the equation r = (3î + 2ĵ )t² m, where 3 and 2 are constants and the time is measured in seconds.

Two-unit vectors A = 3î - 4ĵ and B = 2î + 3ĵ  are given in terms of their components. Determine the magnitude of (i) A and (ii) B.

A particle moving in the wind has a velocity of (17 i - 6j) mph that lasts for 45 min. The wind changes direction affecting the particle velocity. The new velocity is (5i + 18j) mph and lasts for 1.5 h. Calculate the displacement of the particle, giving the result in component form with unit vectors.

What will be the magnitude of -A - 3B when A = i + 2j and B = i - 2j.

For vectors A = 3i + 4j + 5k; B = 4i + 2j + √5 k, what would be the ratio of the magnitude of A to B?

Write down the x-component and y-component for the given vector A = 3.2j - 1.1i

Vector A = -i + 2j. What angle does vector  A = -i + 2j make with the positive direction of x-axis? Let counter-clockwise angles be positive.

You are given two vectors  A = 3i + 4j and B = 6i + 8j; Determine the direction of the vector difference B-A.

Vectors can be written in components; using unit vectors. Determine a vector that shares the same direction as ( î - ĵ ) and has a magnitude of 1.

Use vectors M and N as given in the drawing below. Determine P = M + N, giving the result in component form with unit vectors.

Suppose a velocity vector is represented by vector $\overrightarrow{P}$ = (3.9î−2.8ĵ) m/s. Consider another velocity vector $\overrightarrow{Q}$ =(2.5î+4.7ĵ) m/s. What will be the magnitude and direction of the velocity $\overrightarrow{P}$ - $\overrightarrow{Q}$ ?