HW HELP ASAP PL If a projectile is launched into the air from the ground with an initial velocity of 192 feet per second, how long after launch will the projectile be at a height of 256 feet? Show your work.

Can you use your previous answer to determine how long it will take for the object to reach its maximum height? If so, determine how long it will take and find the maximum height.

How long after launch will the projectile land on the ground? Show your work.

Can you use your previous answer to determine how long it will take for the object to reach its maximum height? If so, determine how long it will take and find the maximum height.

How long after launch will the projectile land on the ground? Show your work.

Below.

Step-by-step explanation:

When provided the initial velocity, and no equation, use

    Use -4.9 for "a" when units is meters.

    Use -16 for "a" when the units is feets

    The initial velocity is the the value of "b"

    If the launch occured from a height (other than the ground), you would add that height as a constant

So, based on given info, here is our equation that models the projectile path:

   h(x) = -16t2 + 192t

   256 = -16t2 + 192t

   0 = -16t2 + 192t - 256

   0 = 16t2 - 192t + 256

   0 = t2 - 12t + 16

   This cannot be factored.

    You can use the quadratic formula, or completing the square, to solve (not shown here)

    Solutions are t =  6 ± 2√5 = 10.47 and 1.53

The height will be at 256 ft after 1.53 seconds and 10.47 seconds

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

go and ask your mom to you