Question # Two particles are released from the same height at an interval of ( 1 mathrm{s} ). How long after the first particle begins to fall will the two particles be ( 10 mathrm{m} ) apart? ( left(g=10 mathrm{ms}^{-2}right) )

# Two particles are released from the same height at an interval of ( 1 mathrm{s} ). How long after the first particle begins to fall will the two particles be ( 10 mathrm{m} ) apart? ( left(g=10 mathrm{ms}^{-2}right) )

(a) ( 1.5 mathrm{s} )

(b) ( 2 mathrm{s} )

(c) ( 1.25 mathrm{s} )

(d) ( 2.5 mathrm{s} )

Solution

( S_{1}=0+frac{1}{2} g(t)^{2} )

( S_{2}=0+frac{1}{2} g(t-1)^{2} )

( ( S_{2}=5 t^{2}+5-10 t )

And ( quad S_{1}-S_{2}=10 )

( 5 t^{2}-left(5 t^{2}-10 t+5right)=10 )

10t - 5 = 10

t = 1.5 sec