crickets can jump with a vertical velocity of up to 14 ft/s. which equation models the height of such a…

crickets can jump with a vertical velocity of up to 14 ft/s. which equation models the height of such a jump, in feet, after t seconds?\n( h(t)=-16 t^{2}+v_{0} t+h_{0} )\n( h(t)=-16 t^{2}+v_{0} t+14 )\n( h(t)=-16 t^{2}+14 t )\n( h(t)=-16 t^{2}+14 t+14 )\nwhat is the maximum height the cricket reaches?\nround to the nearest thousandth.\n( h=square ) feet\ndone

crickets can jump with a vertical velocity of up to 14 ft/s. which equation models the height of such a jump, in feet, after t seconds?\n( h(t)=-16 t^{2}+v_{0} t+h_{0} )\n( h(t)=-16 t^{2}+v_{0} t+14 )\n( h(t)=-16 t^{2}+14 t )\n( h(t)=-16 t^{2}+14 t+14 )\nwhat is the maximum height the cricket reaches?\nround to the nearest thousandth.\n( h=square ) feet\ndone

Answer

Explanation:

Step1: Find the time when maximum height is reached

For a quadratic function (h(t)=at^{2}+bt + c) (here (a=-16), (b = 14), (c = 0)), the time (t) at which the vertex (maximum for (a<0)) occurs is given by (t=-\frac{b}{2a}). [t=-\frac{14}{2\times(-16)}=\frac{14}{32}=\frac{7}{16}]

Step2: Substitute the time into the height function

Substitute (t = \frac{7}{16}) into (h(t)=-16t^{2}+14t). [h(\frac{7}{16})=-16\times(\frac{7}{16})^{2}+14\times\frac{7}{16}] [=-16\times\frac{49}{256}+\frac{98}{16}] [=-\frac{49}{16}+\frac{98}{16}] [=\frac{-49 + 98}{16}=\frac{49}{16}=3.0625]

Answer:

(3.063) feet