Question

a model rocket is launched with an initial upward velocity of 175 ft/s the rocket's height is represented by h (in feet) after t seconds is given by the followingh = 175t - 16t^2find all values of t for which the rockets height id 85 feetand i need to round the answer to nearest hundredth

Answer 1

Given relation between height and time is:

`h=175t-16t^2`

Now put the value of h=85 ft in given relation:

`85=175t-16t^2`

Solving it for t:

`\begin{gathered} 16t^2-175t-85=0 \\ t=\frac{175\pm\sqrt[]{(-175)^2-4*16*85}}{2*16} \\ t=\frac{175\pm\sqrt[]{30625-5440}}{32} \\ t=\frac{175\pm\sqrt[]{25185}}{32} \\ t=(175\pm158.6)/(32) \\ t=0.51\text{ or }10.43\text{ second} \end{gathered}`