Answer

Verified

437.1k+ views

**Hint:**The given case is in a two dimensional system, therefore the directional vectors should also be considered. The total magnitude of the acceleration depends on the acceleration among different directions.

**Complete step by step answer:**

When the two cars are moving in the different directions then the relative velocity of the cars is calculated by subtracting the velocities of the car. When the car moves in directly opposite directions then the relative velocity of the car is calculated by the sum of two velocities.

The direction of the cars is as shown:

The formula to calculate the relative acceleration of car B with respect to car A is

${a_{BA}} = {a_B}\hat j - {a_A}\hat i$

Here, ${a_{BA}}$ is the relative acceleration of car A with respect to car B, ${a_A}$ is the acceleration of car A, $\hat i$ is the unit vector along east direction, ${a_B}$is the acceleration of car B and $\hat j$ is the unit vector along north direction.

Substitute $2\,{{\rm{m}} {\left/{\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right.

} {{{\rm{s}}^{\rm{2}}}}}$ for ${a_A}$ and $4\,{{\rm{m}} {\left/{\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right.} {{{\rm{s}}^{\rm{2}}}}}$for ${a_B}$ in the formula to calculate the relative acceleration of the car B with respect to car A.

${a_{BA}} = \left( {2\,{{\rm{m}} {\left/ {\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right.} {{{\rm{s}}^{\rm{2}}}}}} \right)\hat j - \left( {4\,{{\rm{m}} {\left/{\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right.} {{{\rm{s}}^{\rm{2}}}}}} \right)\hat i$

The formula to calculate the magnitude of relative acceleration of car B with respect to car A is

$\left| {{a_{BA}}} \right| = \sqrt {a_B^2 + a_A^2} \,\,$

Substitute $2\,{{\rm{m}} {\left/{\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right. } {{{\rm{s}}^{\rm{2}}}}}$ for ${a_A}$ and $4\,{{\rm{m}} {\left/{\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right.} {{{\rm{s}}^{\rm{2}}}}}$for ${a_B}$ in the formula to calculate magnitude of the relative acceleration of the car B with respect to car A.

$ \left| {{a_{BA}}} \right| = \sqrt {{{\left( {2\,{{\rm{m}} {\left/{\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right. } {{{\rm{s}}^{\rm{2}}}}}} \right)}^2} + {{\left( {4\,{{\rm{m}} {\left/ {\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right.} {{{\rm{s}}^{\rm{2}}}}}} \right)}^2}} \\

= \sqrt {4 + 16} \,{{\rm{m}} {\left/ {\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right. } {{{\rm{s}}^{\rm{2}}}}}\\

= \sqrt {20} \,{{\rm{m}} {\left/ {\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right.} {{{\rm{s}}^{\rm{2}}}}}\\

= 4.47\,{{\rm{m}} {\left/

{\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right.} {{{\rm{s}}^{\rm{2}}}}} $

Thus, the relative acceleration of car B with respect to car A is $4.47\,{{\rm{m}} {\left/ {\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right.} {{{\rm{s}}^{\rm{2}}}}}$.

**Note:**

The direction of car B relative to car A can also be found from this example because the direction of the car can be calculated using the acceleration of the cars in different directions.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

The polyarch xylem is found in case of a Monocot leaf class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Casparian strips are present in of the root A Epiblema class 12 biology CBSE

How do you graph the function fx 4x class 9 maths CBSE