A rocket which has initial velocity of 64' per second and is on a 8' stand. The formula is H(t) = -16t²+64t +8. Find the height at 1 second. When does it reach its max height? . What is the max height? When does it hit the ground?

a) 56

b) 2 seconds

c) 72

d) 4.12seconds

Step-by-step explanation:

Given the height of the rocket modelled by the equation

H(t) = -16t²+64t +8 where

t is in seconds

a) To find the height at t= 1sec, we will simply substitute t = 1 into the equation as shown;

H(t) = -16t²+64t +8

H(1) = -16(1)²+64(1)+8

H(1) = -16+64+8

H(1) = 64-8

H(1) = 56

Hence the height after 1sec is 56

b) The velocity of the rocket at maximum height is zero, hence;

dH/dt = 0 (at maximum height)

dH/dt = -32t+64

0= -32t+64

32t =64

t =64/32

t =2secs

Hence the rocket reaches its maximum height after 2seconds

c) Substitute t =2 into the equation

H(2) =-16(2)²+64(2)+8

H(2) = -64+128+8

H(2) = 64+8

H(2) = 72

Hence the maximum height is 72

d) The rocket hits the ground when

h(t) =0

Substitute into the equation

0 = -16t²+64t+8

Divide through by -8

0 = 2t²-8t-1

From the equation a =2, b = -8 and c = -1

Using the general formula

t = -b±√b²-4ac/2a

t = -(-8)±√(-8)²-4(2)(-1)/2(2)

t = 8±√64+8/4

t =8±√72/4

t =8±8.49/4

t = 8+8.49/4 and 8-8.49/5

t =16.49/4 and -0.49/4

t = 4.12 and -0.12

Time cannot be negative

Hence t = 4.12secs

The rocket hits the ground 4.12secs later

points are handed out whenever you post answers.

brainliest answers are handed out by the person asking the question, so whether your answer is picked depends entirely on whether the asker bothers to pick

if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )