A car is moving towards east with a speed of 25km/h. To the driver of the car, a bus appears to move towards north with a speed of $25 \sqrt{3} k m / h$ . What is the actual velocity of the bus?

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

$50 k m / h, 30^{0} e a s t o f n o r t h$

$50 k m / h, 30^{0} n o r t h o f e a s t$

$25 k m / h, 30^{0} e a s t o f n o r t h$

$25 k m / h, 30^{0} n o r t h o f e a s t$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

${\vec{υ}}_{c} = 25 \hat{i}, {\vec{υ}}_{b / c} = 25 \sqrt{3} \hat{j}$

${\vec{υ}}_{b / c} = {\vec{V}}_{b} - {\vec{V}}_{c} \Rightarrow {\vec{V}}_{b} = {\vec{V}}_{b / c} + {\vec{V}}_{c}$

$\Rightarrow {\vec{υ}}_{b} = 25 \hat{i} + 25 \sqrt{3} \hat{j}$

$| {\vec{υ}}_{b} | = \sqrt{25^{2} + {(25 \sqrt{3})}^{2}} = 50 k m / h$

$\tan θ = \frac{25}{25 \sqrt{3}} = \frac{1}{\sqrt{3}} \Rightarrow θ = 30^{0}$

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE