1.3 - Vectors & Scalars

A pilot intends to fly a plane from point $A$ to point $B$. Due to strong winds, she points the nose of the plane in the direction shown by the vector $P$. Which of the choices below best represents the direction of the wind encountered by the plane?

Which of the following is a vector quantity?

• A. $\hspace{1em}$ Speed

• B. $\hspace{1em}$ Electric force

• C. $\hspace{1em}$ Electric current

• D. $\hspace{1em}$ Temperature

Vectors $X$ and $Y$ are in the shown directions.

Which of the following shows the sum of the two vectors?

An object moves $9\,m$ east, then $12\,m$ north.

What is the magnitude of the total displacement of this object?

• A. $\hspace{1em}$ 3 $m$

• B. $\hspace{1em}$ 15 $m$

• C. $\hspace{1em}$ 21 $m$

• D. $\hspace{1em}$ 36 $m$

A ball is projected with an initial speed of $2\,m\,s^{-1}$ making an angle of $35^o$ with the horizontal as shown.

Which expression gives the vertical component of the velocity vector?

• A. $\hspace{1em}$ $2\,m\,s^{-1}$

• B. $\hspace{1em}$ $2\,cos(35^o)\,m\,s^{-1}$

• C. $\hspace{1em}$ $2\,sin(35^o)\,m\,s^{-1}$

• D. $\hspace{1em}$ $2\,tan(35^o)\,m\,s^{-1}$

Two trucks X and Y are pulling a car out of thick mud along a straight path. The only other horizontal force acting on the car is a drag force opposite to the direction of motion. The diagram shows the direction of the force applied by truck $X$ and the direction of motion of the car.

Which of the following vectors shows the direction of the force applied by truck $Y$?

Vector $d$ makes an angle $\theta$ with the horizontal as shown. Its magnitude is $5\,m$ and the magnitude of its horizontal component $d_x$ is $3\,m$.

Which of the following is correct about the magnitude and direction of its vertical component?

[Maximum mark: 10]

The circuit shown is used to measure the internal resistance of a cell. The voltmeter and the ammeter used are ideal.

$\footnotesize{\textrm{[Source: Created with GeoGebra, by Tom Walsh - http://ophysics.com/t1.html]}}$

1. 1. Differentiate between precise and accurate measurements. [2]
      

   2. The voltmeter used has a zero error. State the type of uncertainty this will introduce into the voltmeter's measurements. [1]
      

2. 1. The graph shows the variation of the voltmeter's reading with current.

      

      Determine the emf of the cell. [2]
      

   2. Estimate the internal resistance of the cell including its uncertainty. [3]
      

   3. Determine whether the zero error in the voltmeter will affect the calculated value of the internal resistance. Justify your answer. [2]
      

A car moves clockwise in a circular path as shown. The direction of its instantaneous velocity at two different times is shown in the diagram.

Which of the following vectors shows the direction of the change in velocity?

A stream flows east with a speed $v_s$. A boat points due south and moves with a speed $v_o$ relative to the water.

The ratio $\dfrac{v_o}{v_s} = \dfrac{1}{2}$

Which of the following is correct about the magnitude in $m\,s^{-1}$ and the angle $\theta$ between the velocity of the boat and the side of the stream?