Question

Two spherical balls having equal masses with radius of $5\, cm$ each are thrown upwards along the same vertical direction at an interval of $3\, s$ with the same initial velocity of $35\, m / s$, then these balls collide at a height of ______$ m$.
(Take $g =10\, m / s ^{2}$ )

Answer 1

When both balls will collied
$Y_1 = Y_2$
$35 t -\frac{1}{2} \times 10 \times t ^{2}=35( t -3)-\frac{1}{2} \times 10 \times( t -3)^{2}$
$35 t -\frac{1}{2} \times 10 \times t ^{2}=35 t -105-\frac{1}{2} \times 10 \times t ^{2}$
$-\frac{1}{2} \times 10 \times 3^{2}+\frac{1}{2} \times 10 \times 6 t$
$0=150-30 \,t$
$ t =5 \,\sec$
$\therefore $ Height at which both balls will collied
$h =35 t -\frac{1}{2} \times 10 \times t ^{2}$
$=35 \times 5-\frac{1}{2} \times 10 \times 5^{2}$
$ h =50 \,m$