A ball is projected vertically upward with an initial velocity of 50ms^-1 at t = 0s. At t =2 2s, another ball is projected vertically upward with same velocity. At t = _______s, second ball will meet the first ball (g = 10 ms^-2).

<p>&nbsp;<math><mrow><mi>h</mi><mo>=</mo><mn>5</mn><mn>0</mn><mi>t</mi><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mtext>? </mtext><mo>×</mo><mn>1</mn><mn>0</mn><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>8</mn><mn>0</mn><mi>m</mi></mrow></math></p><p><img ></p><p>Now velocity B with respect to A</p><p><math><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>B</mi><mi>A</mi></mrow></msub><mo>=</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>−</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>A</mi></mrow></msub></mrow></math></p><p>= 50 – 30</p><p>= 20 m/sec</p><p>Now&nbsp;<math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>B</mi><mi>A</mi></mrow></msub><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>−</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>A</mi></mrow></msub></mrow></math></p><p>=&nbsp;<math><mrow><mn>1</mn><mn>0</mn><mrow><mo> (</mo><mrow><mo>−</mo><mover accent="true"><mi>j</mi><mo>^</mo></mover></mrow><mo>)</mo></mrow><mo>−</mo><mrow><mo> (</mo><mrow><mo>−</mo><mn>1</mn><mn>0</mn><mover accent="true"><mi>j</mi><mo>^</mo></mover></mrow><mo>)</mo></mrow></mrow></math></p><p><img ></p><p>= 0</p><p>Time taken to collide.</p><p><math><mrow><mi>h</mi><mo>=</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>B</mi><mi>A</mi></mrow></msub><mi>t</mi></mrow></math></p><p>80 = 20t</p><p>t = 4 sec</p><p>Total time = 4 + 2</p><p>= 6 sec</p>

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