Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v₁. The boy at A starts running simultaneously with velocity v and catches the other in time t, where t is equal to:
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Question

Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v₁. The boy at A starts running simultaneously with velocity v and catches the other in time t, where t is equal to:

Options

G1 Physics · Accepted Answer

Step 1: In time t, boy B moves a perpendicular distance v₁t. Step 2: Boy A travels distance vt to the meeting point. These form a right triangle with fixed base a. Step 3: (vt)²=a²+(v₁t)², so (v²−v₁²)t²=a². Hence t=a/√(v²−v₁²). Final answer: D.