Question

A thief runs with a uniform speed of $100m/minute$. After one minute a policeman runs after the thief to catch him. He goes with a speed of $100m/minute$ in the first minute and increases his speed by $10m/minute$ every succeeding minute. After how many minutes the policeman will catch the thief.

Answer 1

$1min\to 2min\to$Relative speed$=(110-100)m/min=10m/min$
$\therefore$ Distance shortened$=10m/min\times 1min=10m=d_1$
$2min\to 3min\to V_{r_2}=120-100=20m/min$
$d_2=20m$
$3\to 4\to d_3=30$
$4\to 5\to d_4=40m$
$d_1+d_2+d_3+d_4=100m$
Distance between cop and thief after $1$ minute$=100m/min\times 1min=100m$
Relative speed between $1min$ and $2min=100-100=0$
Relative speed between $2min$ and $2min=120-100=10m/min$
Relative speed between $3min$ and $3min=20m/min$
Relative speed between $4min$ and $5min=30m/min$
Relative speed between $5min$ and $6min=40m/min$
$10\times 1+20\times 1+30\times 1+40\times 1=100m$
$\therefore after6mins$