1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mila [183]
2 years ago
11

A rocket is launched vertically from the ground with an initial velocity of 64. ft/sec Write a quadratic function that shows the

height, in feet, of the rocket t seconds after it was launched. Graph on the coordinate plane. Use your graph from Part 3(b) to determine the rocket’s maximum height, the amount of time it took to reach its maximum height, and the amount of time it was in the air. Answer:

Mathematics
1 answer:
SpyIntel [72]2 years ago
6 0

Answer:

a. s = 64t - 16t²

a. maximum height = 64 ft

b. time it took to reach maximum height = 2 s

c. total time it spent in the air = 4 s

Step-by-step explanation:

a. Using Newton's third equation of motion under gravity, s = ut - 1/2gt² where s = vertical height of rocket, t = time, u = initial velocity of rocket = 64 ft/s and g = acceleration due to gravity = 32 ft/s².

So, s = 64t - 1/2(32)t² = 64t - 16t²

The equation is thus s = 64t - 16t²

b. The maximum height is obtained when ds/dt = 0

ds/dt = d[64t - 16t²]/dt = 64 - 32t

64 - 32t = 0

32t = 64

t = 64/32 = 2 s

Substituting t = 2 into s, we have

s = 64(2) - 16(2)² = 128 - 64 = 64 ft

c. The amount tot time it took to reach maximum height is 2 s

d. The amount of time it was in the air is obtained when s = 0

s = 0 ⇒

64t - 16t² = 0

16t(4 - t) = 0

16t = 0 or 4 - t = 0

t = 0 or t = 4

So the rocket spends 4 s in the air.

The values of the different variable for a, b,c and d are indicated in the graph.

The point (2,64) indicated the time for maximum height 2 s and maximum height 64 ft.

The point (4,0) indicates the total time spent in the air 4 s

You might be interested in
What property is illustrated in this equation?
Lerok [7]
In the equation given, the Distributive Property is being demonstrated.
8 0
3 years ago
3x+8=2x+21<br> X=?<br> (all working out needed)
Dahasolnce [82]

Answer:

x=13

Step-by-step explanation:

3x=2x+21−8

3x=2x+13

3x−2x=13

x=13

8 0
2 years ago
Read 2 more answers
Which equation represents a line which is perpendicular to the line 4x + 3y = - 24 ?
Scorpion4ik [409]

Answer:

C

Step-by-step explanation:

4x+3y=-24

eq. of any line perpendicular to given line is

3x-4y=a

4y=3x-a

y=3/4x -a/4

where a is an arbitrary constant.

4 0
2 years ago
Imagine that you are standing at the top of a cliff that is 1,500 feet above sea level. You see ship A, and your eyes make an an
kati45 [8]
Answer: option A. 30 °.

Explanation:

1) Draw this triangle: Eyes - Ship A - height of the cliff:

The angle of the vertix where the eyes are is: 90° - depreesion angle = 90° - 60° = 30°.

2) opossite leg = horizontal distance to the ship A = x

3) adjacent leg = height of the cliff = 1500 feet

4) tan(30°) = x / 1500 feet => x = 1500 tan(30°) = 1500 √3 / 3 = 500√3

5) Draw the triangle of the eyes - ship B - hieght of the cliff

6) The unknown is the depression angle of the eyes with ship B, α

7) opposite leg = 500√3 feet + 1000√3 feet = 1500√3 feet

8) adjacent leg = height of the cliff = 1500 feet

9) tan(α) = opposite leg / adjacent leg = 1500√3 / 1500 = √3

10) α = arctan(√3) = 60°

11) Depression angle = 90° - 60° = 30° Which is the answer

5 0
3 years ago
Read 2 more answers
What is the second smallest number that has 1,2,3,4,and 5?
n200080 [17]

Answer:

12354

Step-by-step explanation:

The smallest number with 12345  (I am assuming with out decimals) is

12345

If we switch the 5 and 4  we will get the second smallest number

12354

4 0
2 years ago
Read 2 more answers
Other questions:
  • I need help with the whole homework and yeah plz answer and who ever answers gets a brainlist answer
    5·1 answer
  • Sara has a loan for $1800 at a rate of 16% annually. How much interest will she pay in 4 years?
    14·1 answer
  • A necklace is made of 12 red beads and 18 orange beads. How many red beads would be needed to make the same necklace with 90 ora
    10·2 answers
  • CAN SOMEONE HELP ME PLEASE??
    13·1 answer
  • One, no, or infinitely many solutions?
    15·1 answer
  • Todd Lyle worked Monday through Friday from 8:00 A.M. to 5:00 P,M. with an hour off for lunch. He is paid $10,50 an hour. Find h
    15·1 answer
  • In the rope climb, a 75 kg athlete climbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was used to accomplis
    14·1 answer
  • In 3 3/4hours one day in February, it snowed 3 feet in Amarillo. How much snow fell per hour?
    15·1 answer
  • PLEASE HELP!!!!! 1.) Line a passes through points (-2, 1) and (2, 9). Write an equation in slope intercept form that is parallel
    7·2 answers
  • Help me please I need to turn this in at 10:50 PM
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!