A particle is moving along a projectile path where the initial height is 96 feet with an initial speed of 16 feet per second. What is the maximum height of the particle? 100 feet 96 feet 60 feet 56 feet

Answer:The maximum height of the particle is 100 ftA is correctStep-by-step explanation:A particle is moving along a projectile path where the initial height is 96 feet with an initial speed of 16 feet per second.The standard equation of parabolic projectile.[tex]h(t)=-16t^2+v_0t+h_0[/tex]where, [tex]v_0=16\ ft/s[/tex][tex]h_0=96\ ft[/tex][tex]h(t)=-16t^2+16t+96[/tex]So, we get the parabolic equation of path. The maximum value at vertex. [tex]t=-\dfrac{b}{2a}[/tex][tex]t=-\dfrac{16}{-32}=\dfrac{1}{2}[/tex]Maximum at t=0.5[tex]h(0.5)=-16(0.5)^2+16(0.5)+96[/tex][tex]h(0.5)=100[/tex]Hence, The maximum height of the particle is 100 ft