Question

matt shoots a trick basketball shot upwards according to equation h=16t³+32t²=48t where h is the height of ball in feet,and t is the time in seconds .how long will take for Matts ball to hit the ground

Answer 1

        $\text{The given equation is:-}$

        $f(t) = h = 16t^{3} + 32t^{2} - 48t$

        $\text{We have to find the value of }t \text{ when }h = 0$

$\implies \: 16t^3 + 32t^2 - 48t = 0$

$\implies \: t(16t^2 + 32t - 48) = 0$

$\implies \: t = 0 \; \; ; \; \; 16t^2 + 32t - 48 = 0$

        $\text{Since }t = 0 \text{ refers to the starting point we can neglect it}$

$\implies \: 16t^2 + 32t - 48 = 0$

$\implies \: t^2 + 2t - 3 = 0$

$\implies \: t^2 + 3t - t - 3 = 0$

$\implies \: t(t + 3) - 1 (t+3) = 0$

$\implies \: (t+3)(t-1) = 0$

$\implies \: t = 1,-3 \: s$

        $\text{Time cannot be negative}$

$\implies \: \boxed{t = 1 \: s}$