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If an archer shoots an arrow straight upward with an initial velocity of 160

ft/sec from a height of 8 feet, its height above the ground in feet at time t in seconds is

given by the function h(t)= -16t^2+160t +8. What is The maximum height reached by the arrow

Respuesta :

Answer:

maximum height of the arrow will be 408 m

Step-by-step explanation:

We have given the function of height as [tex]h(t)=-16t^2+160t+8[/tex]

We know that first derivative of height will be velocity

So first derivative of height

[tex]\frac{dh}{dt}=-32t+160[/tex]

[tex]v(t)=-32t+160[/tex]

We know that at maximum height velocity will be zero

[tex]-32t+160=0[/tex]

t = 5 sec

Sp arrow will be at maximum height at t = 5 sec

So height at t = 5 sec will be

[tex]h(5)=-16\times 5^2+160\times 5+8=408m[/tex]

So maximum height of the arrow will be 408 m

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