Two car A and B are ,moving with their velocity 20m/s and 30m/s east and west respectively. if they started from the same place at same time. what would be the distance between them after 2 min/find the distance covered by each other at the same time.
Answers
Answer:
Explanation:
11th
Physics
Motion in a Plane
Relative Motion in 2 Dimension
Two cars A and B are mo...
PHYSICS
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Asked on December 27, 2019 by
Sapan Guda
Two cars A and B are moving west to east and south to north, respectively, along crossroads. A moves with a speed of 20ms
−1
and is 500m away from the point of intersection of cross roads and B moves with a speed of 15ms
−1
and is 400m away from the point of intersection of cross roads. Find the shortest distance between them.
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ANSWER
Using the concept of relative velocity
Let us assume the velocity of A w.r.t. B. To do this, we plot the resultant velocity,
V
→
AB
V
→
AB
=
V
→
A
−
V
→
B
=
V
→
A
+(−
V
→
B
)
As the accelerations of both the cars is zero, so the relative acceleration between them is also zero. Hence, the relative velocity will remain constant. So the path of A with respect to B will be straight line and along the direction of relative velocity of A with respect to B. The shortest distance between A and B is a perpendicular from B on the line of motion of A with respect to B.
From the figure
tanθ=
V
A
V
B
=
20
15
=
4
3
....(i)
This θ is the angle made by the resultant velocity vector ∣
V
→
AB
∣ with the x-axis.
Also we know that from Fig.
OC=
500
x
=
4
3
From equation (i) and (ii), we get x = 375 m.
∴AB=OB−OC=400−375=25m
But the shortest distance is BP.
From diagram, it is clear that BP=BCcosθ=25×
5
4
∴BP=20m