Postion of an object at a given time?

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In summary, the conversation involves a problem with a rocket accelerating straight upward from rest with constant net acceleration, until the fuel is exhausted. The equation for this is given, and it is noted that the initial velocity and position are both zero. The problem is to find the height when the fuel is burnt and the velocity at that time. The answer is 368 meters, but the conversation discusses a possible error and suggests finding the velocity at t_1 and using that to solve for the distance traveled after the fuel is burned out. The next question involves determining whether the velocity and acceleration of a power ball are positive, negative, or zero based on a given figure. The correct answer is p, n.
  • #1
badman
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im trying to do this problem involving the postion of a rocket going straight up at a given time.

it says a rocket initially at rest on the ground, accelerates straight upward from rest with constant net acceleration a, until time t(subscript 1) when the fuel is exhausted.

the equation for this is: position at that time=initial position+initial velocity times t(time)+0.5 times 3 times 9.81m/s^2 times T^2

i know initial velocity and position are zero, so all i got left over is the rest of the equation.

a=3g(g being accel. due to gravity) and T(subscript 1)=5.00s
it says to give ur answer in meters. i ended up with 368 meters. but it said that i forgot a numerical factor?
 
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  • #2
[tex]x = \frac{1}{2} at^2 = \frac{1}{2} (3*9.8)(5)^2 = 367.5m[/tex]
 
  • #3
thats what i basically entered but it keeps saying that I am off by a numerical factor? why the hell does it keep saying that.

the height I am supose to give is in this form H (subscript) 3= the answer.

it also says express the answer numerically in meters using g=9.81 m/s^2. just to be clear on that. i don't know what's the problem
 
  • #4
I don't think this has to do with sig figs.

Compute the velocity at the time when all the fuel is burnt.From then on,the rocket goes straight up due to inertia.Gravity will be then the only force acting on it.

Your number ~368 is too small.

Daniel.
 
  • #5
Are you trying to find the height when the fuel is burnt, or the final height? If its the first, then 368 is the answer.
 
  • #6
it says to look for the maximum height
 
  • #8
In that case find the velocity at t_1, then use the same equation you gave above with v_0 = v(t_1) and a = -9.8

Solve v_0 - at = 0 for a = 9.8 and v_0 = v(t1) to find where the velocity is 0 (the top). Use that value for t.

This is the distance traveled after the fuel is burned out.
 
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  • #9
how would i go about computing the velocity at T_1.?
 
  • #10
You underwent constnat acceleration of 3*9.8 for 5 seconds.
 
  • #11
thanks for the help. guys.

i have another quetion, but i don't know how to type these leters the right way

The next figure View Figure shows the velocity vectors corresponding to the upward motion of the power ball. Indicate whether its velocity and acceleration, respectively, are positive (upward), negative, or zero.
Use P, N, and Z for positive (upward), negative, and zero, respectively. Separate the letters for velocity and acceleration with a comma.

i tried typing in v p, a n, and other combnations but said it had the wrong number of terms separated by commas. how do i go about typing these terms in?


heres a the figure there referring to.
 

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  • #12
I think its looking for just p, n
Those are correct answers.
 
  • #13
thanks a lot man, that helped with the next problem. i really didnt know how to input these terms in.
 

Related to Postion of an object at a given time?

What is the position of an object at a given time?

The position of an object at a given time is its location in space at a specific moment. It is typically described using coordinates, such as distance, direction, and elevation.

What factors determine the position of an object at a given time?

The position of an object at a given time is determined by its initial position, velocity, and acceleration. Other factors such as external forces and environmental conditions may also play a role.

How is the position of an object at a given time calculated?

The position of an object at a given time can be calculated using mathematical equations and principles, such as Newton's laws of motion, kinematics, and calculus. It may also require the use of specialized tools and technologies, such as GPS or motion sensors.

Why is it important to know the position of an object at a given time?

Knowing the position of an object at a given time is crucial in various fields, including physics, engineering, and navigation. It allows us to understand and predict the motion of objects, design structures and machines, and accurately navigate through space.

Can the position of an object at a given time change?

Yes, the position of an object at a given time can change due to various factors, such as its velocity, acceleration, and external forces. This change in position is known as displacement and can be either positive or negative, depending on the direction of the object's motion.

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