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A ship A is moving westward with a speed of 10km /h -1 and ship B 100km south of A is moving northward with speed of 10km h-1 the time after which the distance between. Them become shortest is a) 0h b)5h c)5√2h d)10√2h?
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A ship A is moving westward with a speed of 10km /h -1 and ship B 100k...
**Given Information:**
Ship A is moving westward with a speed of 10 km/h.
Ship B is 100 km south of A and is moving northward with a speed of 10 km/h.
**Finding the Shortest Distance:**
To find the shortest distance between the two ships, we can imagine a right-angled triangle formed by the two ships and the shortest distance between them as the hypotenuse of the triangle.
Let's consider the time t after which the distance between the two ships is the shortest.
**Ship A's Position:**
Since Ship A is moving westward with a speed of 10 km/h, its position can be represented as:
x_A = -10t
**Ship B's Position:**
Since Ship B is 100 km south of A and is moving northward with a speed of 10 km/h, its position can be represented as:
y_B = 100 - 10t
**Distance between the Ships:**
The distance between the two ships can be calculated using the distance formula:
d = sqrt((x_B - x_A)^2 + (y_B - y_A)^2)
Substituting the positions of the ships:
d = sqrt((-10t)^2 + (100 - 10t)^2)
Simplifying:
d = sqrt(100t^2 + 10000 - 2000t + 100t^2)
d = sqrt(200t^2 - 2000t + 10000)
**Finding the Time for Minimum Distance:**
To find the time t after which the distance between the two ships is the shortest, we can differentiate the distance function with respect to time and equate it to zero:
d/dt sqrt(200t^2 - 2000t + 10000) = 0
Simplifying:
(200t^2 - 2000t + 10000)' = 0
400t - 2000 = 0
400t = 2000
t = 5 hours
**Therefore, the time after which the distance between the two ships becomes the shortest is 5 hours.**
The correct answer is option b) 5h.
Ship A is moving westward with a speed of 10 km/h.
Ship B is 100 km south of A and is moving northward with a speed of 10 km/h.
**Finding the Shortest Distance:**
To find the shortest distance between the two ships, we can imagine a right-angled triangle formed by the two ships and the shortest distance between them as the hypotenuse of the triangle.
Let's consider the time t after which the distance between the two ships is the shortest.
**Ship A's Position:**
Since Ship A is moving westward with a speed of 10 km/h, its position can be represented as:
x_A = -10t
**Ship B's Position:**
Since Ship B is 100 km south of A and is moving northward with a speed of 10 km/h, its position can be represented as:
y_B = 100 - 10t
**Distance between the Ships:**
The distance between the two ships can be calculated using the distance formula:
d = sqrt((x_B - x_A)^2 + (y_B - y_A)^2)
Substituting the positions of the ships:
d = sqrt((-10t)^2 + (100 - 10t)^2)
Simplifying:
d = sqrt(100t^2 + 10000 - 2000t + 100t^2)
d = sqrt(200t^2 - 2000t + 10000)
**Finding the Time for Minimum Distance:**
To find the time t after which the distance between the two ships is the shortest, we can differentiate the distance function with respect to time and equate it to zero:
d/dt sqrt(200t^2 - 2000t + 10000) = 0
Simplifying:
(200t^2 - 2000t + 10000)' = 0
400t - 2000 = 0
400t = 2000
t = 5 hours
**Therefore, the time after which the distance between the two ships becomes the shortest is 5 hours.**
The correct answer is option b) 5h.
Community Answer
A ship A is moving westward with a speed of 10km /h -1 and ship B 100k...
A) 5 hrs.
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A ship A is moving westward with a speed of 10km /h -1 and ship B 100km south of A is moving northward with speed of 10km h-1 the time after which the distance between. Them become shortest is a) 0h b)5h c)5√2h d)10√2h?
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A ship A is moving westward with a speed of 10km /h -1 and ship B 100km south of A is moving northward with speed of 10km h-1 the time after which the distance between. Them become shortest is a) 0h b)5h c)5√2h d)10√2h? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A ship A is moving westward with a speed of 10km /h -1 and ship B 100km south of A is moving northward with speed of 10km h-1 the time after which the distance between. Them become shortest is a) 0h b)5h c)5√2h d)10√2h? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ship A is moving westward with a speed of 10km /h -1 and ship B 100km south of A is moving northward with speed of 10km h-1 the time after which the distance between. Them become shortest is a) 0h b)5h c)5√2h d)10√2h?.
A ship A is moving westward with a speed of 10km /h -1 and ship B 100km south of A is moving northward with speed of 10km h-1 the time after which the distance between. Them become shortest is a) 0h b)5h c)5√2h d)10√2h? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A ship A is moving westward with a speed of 10km /h -1 and ship B 100km south of A is moving northward with speed of 10km h-1 the time after which the distance between. Them become shortest is a) 0h b)5h c)5√2h d)10√2h? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ship A is moving westward with a speed of 10km /h -1 and ship B 100km south of A is moving northward with speed of 10km h-1 the time after which the distance between. Them become shortest is a) 0h b)5h c)5√2h d)10√2h?.
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