Problema Solution
The height h (in feet) of a rider on the Big Shot can be modeled by h= -16t^2+v0(t)+921 where t is the elapsed time (in seconds) after launch and v0 is the initial vertical velocity (in feet per second). Find vo using the fact that the maximum value of h is 921+160=1081 feet.
Answer provided by our tutors
Vo = the initial vertical velocity is the constant we need to find
since we know that the quadratic y = ax^2 + bx + c with a<0 has maximum value at its vertex equal to c - (b^2/4a) we have
h(t) = - 16t^2 + Vo*t + 921 has negative quotient in front of t^2 that is a = -16 <0 thus it has maximum value equal to
(c - b^2/4a), where c = 921, b = Vo and a = -16
we also know that the maximum value equals 1081
921 - Vo^2/(4*(-16)) = 1081
Vo^2/64 = 1081 - 921
Vo^2 = 160*64
Vo = 32*(10^0.5) ft/s
Vo = 101.19 ft/s
the initial vertical velocity is 101.19 ft/s.