can you help me?

[confusedfreshman]

Q#1: suppose a rocket takes 17 seconds to return to Earth after launching. Explain how to find the time it takes the rocket to reach its maximum height.

Q#2: explain how to work backword from second differences to extend a sequence.

Q#3: find the first and second differences for the sequence 20,27,36,47,60.

 

[soroban]

Hello, confusedfreshman!

Q#1: suppose a rocket takes 17 seconds to return to Earth after launching.
Explain how to find the time it takes the rocket to reach its maximum height.

There is a formula and some algebra required, but here's an intuitive answer.

Assuming the rocket is launched from ground level (height = 0),
. . it reaches maximum height at t = 17/2 = 8.5 seconds . . . exactly <u>half</u> the flight time.

Q#3: find the first and second differences for the sequence: 20, 27, 36, 47, 60.

We have: . 20 . . 27 . . 36 . . 47 . . 60
. . . . . . . . . . .\ . / . \ . ./ . .\ . / . \ . /
First diff: . . . . 7 . . . 9 . . . 11 . .13
. . . . . . . . . . . . .\ . ./ . \ . ./ . \ . /
Second diff: . . . . 2 . . . 2 . . . 2

 

[confusedfreshman]

thank you

 

[Gene]

I'm afraid Soroban's intuition is faulty. It works for bullets, not for rockets.
My rocket accelerates at 1.00000001g
It rises to a maximum height of much less than an inch and reaches that height in about 17 seconds.
My other rocket accelerates at 1000000g for almost no time (like a bullet) to the same speed with which it hits. Then Sorobans answer is correct.
There is no fixed answer. It can be anything between the two answers.

 

[soroban]

Good point, Gene!

I overlooked the word "rocket", which implies a propulsion system.

With an acceleration involved (even downward), all bets are off . . .