A man wants to reach from A to the opposite corner of the square C (Fig) . The sides of the square are 100 m. A central square of 50m is filled with sand. Outside this square, he can walk at a speed 1 m/s. In the central square, he can walk only at a speed of v m/s (v < 1). What is smallest value of v for which he can reach faster via a straight path through the sand than any path in the square outside the sand?
0.18 ms−1
0.87 ms−1
0.81 ms−1
0.95 ms−1
A
0.18 ms−1
B
0.87 ms−1
C
0.81 ms−1
D
0.95 ms−1
Open in App
Solution
Verified by Toppr
AC=√(100)2+(100)2 = 100√2m
PQ=√(50)2+(50)2 = 50√2m
AP=AC−PQ2=100√2−50√22 = 25√2m
RC=AR=25√2m
Consider the straight-line path APQC through the sand. Time is taken to go from A to C via this path
Tsand =AP+QC1+PQv= 25√2+25√21+50√2v
=50√2[1v+1]
The shortest path outside the sand will be ARC. Time is taken to go from A to C via this path
Toutside= AR+RC1= 25√10+25√101
=50√10
∵Tsand < Toutside
∴50√2[1v+1] < 50√10
⇒1v+1<√5
or 1v<√5−1
orv>1√5−1=0.81ms−1
Was this answer helpful?
2
Similar Questions
Q1
A man wants to reach from A to the opposite corner of the square C (Fig) . The sides of the square are 100 m. A central square of 50m is filled with sand. Outside this square, he can walk at a speed 1 m/s. In the central square, he can walk only at a speed of v m/s (v < 1). What is smallest value of v for which he can reach faster via a straight path through the sand than any path in the square outside the sand?
View Solution
Q2
A man can swim in still water with a speed of 2ms−1. If he wants to cross a river of water current speed √3ms−1 along shortest possible path, then in which direction should he swim?
View Solution
Q3
A river is flowing from west to east with a speed 5 ms−1. A swimmer can swim in still water at a speed of 10 ms−1. If he wants to start from point A on south bank and reach opposite point B on north bank, in what direction should he swim?
View Solution
Q4
A man usually gets from one corner of a square lot to the opposite corner by walking along two of the sides. Approximately what percent of the distance does he save if he walks along the diagonal?
View Solution
Q5
The root mean square speed of 8g of He is 300ms−1. Total kinetic energy of He gas is: