an arrow is shot into the air with an initial velocity of 96 feet per second. the height in feet of the arrow t seconds after it was shot into the air is given by the function h(x)=-16t^2+96t. find the maximum height of the arrow. what is the answer

how long was the arrow in the air

how long was the arrow in the air

answers

Well, the maximum height of the arrow is quite high. It's so high that if you threw a party up there, even the birds would have to RSVP! But let me do some math to figure out the exact answer for you.

To find the maximum height, we need to determine the vertex of the parabolic function h(t) = -16t^2 + 96t. The vertex formula tells us that the t-coordinate of the vertex is given by -b/2a, where a = -16 and b = 96.

So, substituting the values into the formula, we get:

t = -96/(2*(-16))
t = -96/(-32)
t = 3

Now that we know the time, we can find the height by plugging it back into the function:

h(3) = -16(3)^2 + 96(3)
h(3) = -144 + 288
h(3) = 144

So, the maximum height of the arrow is 144 feet. That's quite impressive! It's like the arrow reached for the stars but settled for the clouds instead.

To find the maximum height of the arrow, we need to determine the vertex of the parabolic function. The vertex represents the highest point of the parabola, which in this case corresponds to the maximum height.

The general form of a quadratic function is given by f(x) = ax^2 + bx + c. Comparing this with our given function, h(x) = -16t^2 + 96t, we can identify that a = -16, b = 96, and c = 0.

The x-coordinate of the vertex can be found using the formula x = -b/2a. Substituting the values, we have:
x = -(96) / (2*(-16))
x = -96 / (-32)
x = 3

Therefore, the arrow reaches its maximum height at t = 3 seconds.

To find the maximum height itself, we substitute t = 3 into the function h(t):
h(3) = -16(3)^2 + 96(3)
h(3) = -16(9) + 288
h(3) = -144 + 288
h(3) = 144 feet

Hence, the maximum height of the arrow is 144 feet.

h(x) = -16t^2 + 96t.

The parabola opens downward. Therefore,
the max. point is the vertex.

t(V) = -b/2a = -96 / -32 = 3s = The value of t at the vertex.

h=-16*3^2 + 96*3 = -144 + 288 = 144Ft


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