Question

A car is moving with a constant velocity of 60 m/s towards north and
a truck is moving with a constant velocity of 80 m/s towards east.
The magnitude of relative velocity of car writ, truck will be​

Answer 1

$\underline{ \boxed{ \mathfrak{ \huge{ \orange{Answer}}}}} \\ \\ \star \: \blue{ \rm{Given}} \\ \\ \implies \rm\: velocity \: of \: car = 60 \: \hat{j} \\ \\ \implies \rm \: velocity \: of \: truck = 80 \: \hat{i} \\ \\ \star \: \blue{ \rm{To \: Find}} \\ \\ \implies \rm \: relative \: velocity \: of \: car \: wrt \: truck \\ \\ \star \: \blue{ \rm{Formula}} \\ \\ \: \: \: \: \: \: \underline{ \huge{\boxed{ \pink{ \rm{V{ \tiny{ct}} = V{ \tiny{c}} - V{ \tiny{t}}}}}}} \\ \\ \star \: \blue{ \rm{Calculation}} \\ \\ \mapsto \rm \: V{ \tiny{ct}} = 60 \hat{j} - 80 \hat{i} = \sqrt{ {60}^{2} + {80}^{2} } = 100 \: \frac{m}{s} \\ \\ \\ \underline{\boxed{ \mathfrak{ \red{V{ \tiny{ct}} = 100 \frac{m}{s} \: at \: north \: east \: direction}}}}$

Answer 2

GIVEN :

• Velocity of Car = 60 m/s
• Velocity of Truck = 80 m/s

TO FIND :

• Magnitude of relative velocity of car with truck

Solution :

$\boxed { \blue{\bf {V}_{ab} = \bf \sqrt{ {({V}_{a})}^{2} + {({V}_{b}}^{2} )} } } \\ \\ \bf {V}_{ab} = \sqrt{ {60}^{2} + {80}^{2} } \\ \\ \bf {V}_{ab} = \sqrt{3600 +6400} \\ \\ \bf {V}_{ab} = \sqrt{10000}$

$\large \underline { \boxed { \bf \orange{{ V}_{ab} = 100 \: {ms}^{ - 1} }}}$