time = 32.1 seconds.
Step-by-step explanation:
Remark.
The very first thing about this question that you must understand is that only the vertical part of the 550 feet per second matters.
That's the part of the velocity that works against gravity. The object of this question is this: how long does it take for the rocket to get from 550 feet per second to 0 when the rocket will stop and begin to fall back to earth?
t = 32.1 seconds is the answer.
Step One
Find the vertical velocity.
The formula for the vertical speed is V_vertical = 550 * Sin(70)
Vv = 516.8 feet per second. That is just a formula for finding the vertical velocity.
Step Two
What is the acceleration for this question?
You have no doubt heard the expression "What goes up much come down."
It is certainly true on planet earth. The force of gravity always acts downwards. The rocket's velocity is acting upwards. That's why the rocket goes up in the first place. The measurement for acceleration is 32.2 feet / second^2 and it is downwards.
The meaning of that number is that for every second that an object is moving up, it loses a velocity amount of 32 feet/sec. So the rocket is slowing down.
Step Three
Write your givens and what you need.
t = ??
vi = 516.8 feet / sec
a = - 32.2 feet / sec ^2
vf = 0
Step Four
What is the formula
a = (vf - vi)/t  or in this case
t = (vf - vi/a
Step Five
Solve using the givens.
t = (0 - (+)516.8)/-32.2
t = (0 - 516.8)/-32.2
t = - 516.8 / - 32.2
t = 16.05 seconds
Step Six
That is the time taken to go to the maximum height. Physics says that it will take the same amount of time to come down. The total time in the are = 2 * 16.05 = 32.1 seconds
So your answer is 32.1 seconds.
Note
There is absolutely no other way to do this problem. You should never have been given it without some sort of background in physics. All of the facts I have used have to be verified by experiment. These are
1. Only the vertical velocity matters. It is found by Vv = V* sin(70)
2. The acceleration due to gravity acts down.
3. The value of the acceleration = 32.2 feet/sec^2
4. The time take to complete 1/2 the journey (up to where the rocket stops) is 16.05 seconds.
5. The total time is double the going up time.
Note Two
You might be able to do this by means of energy, but that also involves physics and the time would have to be determined using this approach anyway.
I pass this along to see if anyone can do it using non-physics methods. If they can, I'll tip my hat in their direction.
