SATHEE: Motion in a Plane - Result Question 42

Motion in a Plane - Result Question 42

45. A ship A is moving Westwards with a speed of $10 k m h^{- 1}$ and a ship B $100 k m$ South of A, is moving Northwards with a speed of $10 k m h^{- 1}$ . The time after which the distance between them becomes shortest, is :

[2015]

(a) $5 h$

(b) $5 \sqrt{2} h$

(d) $0 h$

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Answer:

Correct Answer: 45. (a)

Solution:

(a) Let $t$ be the time passed and $x$ be distance covered by the two ships after which the distance between them becomes shortest.

distance(s) between the ship is given by,

$S = \sqrt{(100 - x)^{2} + x^{2}}$

For $S$ to be minimum, $\frac{d s}{d t} = 0$

$\begin{aligned} \Rightarrow \frac{d s}{d t} = \frac{1}{9 [(100 - x)^{2} + x^{2}]^{- 1 / 2}} \\ \Rightarrow 4 - 2 (100 - x) + 2 x] = 0 \\ 4 x - 200 = 0 \Rightarrow x = 50 m \end{aligned}$

So, after both the ships have covered $50 m$ , distance between them becomes shortest. Time taken for it, will

$t = \frac{x}{10} = \frac{50}{10} = 5 h r .$

Motion in a Plane - Result Question 42

45. A ship A is moving Westwards with a speed of $10 k m h^{- 1}$ and a ship B $100 k m$ South of A, is moving Northwards with a speed of $10 k m h^{- 1}$ . The time after which the distance between them becomes shortest, is :

Answer:

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Motion in a Plane - Result Question 42

45. A ship A is moving Westwards with a speed of 10kmh−1 and a ship B 100km South of A, is moving Northwards with a speed of 10kmh−1. The time after which the distance between them becomes shortest, is :

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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45. A ship A is moving Westwards with a speed of $10 k m h^{- 1}$ and a ship B $100 k m$ South of A, is moving Northwards with a speed of $10 k m h^{- 1}$ . The time after which the distance between them becomes shortest, is :