How long will it take to reach 3km?

  • Thread starter speedy46
  • Start date
  • Tags
    Time
In summary: Good job.Find the time taken to reach a height of 3 km.In summary, using the given information of a jet aircraft climbing at a 90 degree angle to the horizontal with a thrust of 90kN, a mass of 8 tonne, and an air resistance of 11kN, the time taken to reach a height of 3 km starting from a speed of 160 km/h is approximately 63.99 seconds. This was calculated by finding the net force, acceleration, and using the equations for displacement and velocity.
  • #1
speedy46
46
0

Homework Statement



A jet aircraft climbs in a straight line at an attitudeof 90 degrees to the hozizontal. The jet thrust amounts to 90kN, the mass of the aircraftis 8 tonne and the average air resistance mounts to 11kN. Calculate the time taken to reach a height of 3 km if the speed at the start of the climb is 160Km/h.


Homework Equations



u= 160km/hr = 44.4 m/s
a= to be calculated
s= 3000m
t=

S=u*t+ 1/2 at^2


F= m times a


The Attempt at a Solution



vertical acceleration force
79 cos 60 - 8000kg

F=ma

a=f / m

0 = (1/2a) t^2 + (u) t + s
0 = 2.435t^2 + 138.56 t - 3000

am confused.
 
Physics news on Phys.org
  • #2
Hi speedy. I'm a bit confused too... you have that the aircraft is climbing at an attitude of 90 degrees to the horizontal. That tells me it's going straight up. Is that right? Or is the 90 degrees a typo?

Regardless of if it's a typo or not, it seems like you have the right equations. Just have to solve them. The thing you're trying to determine is acceleration. To do that, sum the forces in the direction of motion of the aircraft first. What forces are pushing back or resisting the forward motion of the aircraft? What forces are pushing the aircraft forward or tending to accelerate the aircraft? Try drawing a picture of the aircraft with forces acting on it if you're still confused, then try to resolve what those forces are.

Those forces are resisted by the mass of the aircraft, so you should be able to solve the acceleration by summing the forces and then dividing by the mass of the aircraft.

Once you determine the acceleration, stick that into your equation:
S=u*t+ 1/2 at^2

And solve for time.
 
  • #3
Nope the 90 degrees is not a typo

I will be am going to have a go then post my workings out to see if there correct
 
  • #4
Then why did you multiply by cos(60 deg)? Also, mass is not force; you cannot subtract mass from force. Plus your units are currently inconsistent. Convert all numeric values to consistent units.
 
  • #5
Net force = 9000 - 89000 = 600N

F=ma

a=600/800 = 0.075m/s^2

V^2=U^2+as

V^2= (44.44^2) + (2*0.075*300)
V= 49.24m/s

t=V-U/a = 49.24 - 44.44 / 0.075 = 63.99s

Could you please tell me if this is right

Thanks In advance
 
  • #6
speedy46 said:
Net force = 9000 - 89000 = 600N
9000-89000 is not 600
Looks like you typed something wrong, but it's not obvious where the mistake is.

a=600/800 = 0.075m/s^2
600/800 is not 0.075.
It looks like you meant either 600/8000, or you meant 0.75

Please try to proofread your posts. If you see little math mistakes like these, you can still edit it and correct the simple stuff. It is difficult to follow your thought process if you keep typing in the wrong numbers.

It's just a matter of being more careful. Then we can help.
 
  • #7
I have changed my lay out hope this is better for you to follow:-

Conversions.

8000 × 9.8 = 78400N
160Km/h = 44.44m/s

Equations Needed.

F = m × a

S = u × t + 0.5 × a × t2

The solution.

Net Force = Jet thrust – (air resistance + weight of plane)
Net force = 90000N – (11000N + 78400) = 600N

Working out the acceleration.

F = m × a

a = f ÷ m

= 600 ÷ 8000 = 0.075 m/s2

Working out the time.

V2 = u + 2 × a × s

V2 = (44.442) + (2 × 0.075 × 3000)

V2 = 49.24m/s


v = u + a × t

t = v – u ÷ a

t = 49.24 – 44.44 ÷ 0.075

t = 63.99s

Thanks in advance
 
  • #8
That answer looks right.

Things got a little sloppy here, but you probably just copied down things differently from where you worked this out on paper:
speedy46 said:
V2 = u + 2 × a × s

V2 = (44.442) + (2 × 0.075 × 3000)

V2 = 49.24m/s

Should be V^2 = u^2 + 2×a×s,
but V=49.24 m/s is correct.
 

FAQ: How long will it take to reach 3km?

What is the formula for calculating time taken?

The formula for calculating time taken is: Time Taken = Distance / Speed. This formula is based on the basic equation of speed which is Speed = Distance / Time. By rearranging the equation, we can solve for time.

How do I convert time taken from one unit to another?

To convert time taken from one unit to another, we can use the conversion factor of 1 hour = 60 minutes = 3600 seconds. For example, if we want to convert 2 hours to minutes, we can multiply 2 by 60 to get 120 minutes. Similarly, to convert 2 hours to seconds, we can multiply 2 by 3600 to get 7200 seconds.

What factors can affect the accuracy of time taken calculations?

Factors that can affect the accuracy of time taken calculations include human error, measurement error, and external factors such as traffic or weather conditions. It is important to take these factors into consideration when conducting experiments or analyzing data.

How can I improve the accuracy of my time taken calculations?

To improve the accuracy of time taken calculations, it is important to minimize human and measurement error by using precise instruments and methods. Additionally, conducting multiple trials and averaging the results can help to reduce the impact of external factors on the accuracy of the calculations.

What are some real-world applications of calculating time taken?

Calculating time taken has many real-world applications, such as in the fields of physics, engineering, and sports. It is used to measure the speed of objects, determine the efficiency of machines, and track performance in athletic events. Time taken calculations are also important in everyday tasks, such as planning travel time or estimating delivery times.

Similar threads

Back
Top