# Calclulating time taken

1. Jan 20, 2009

### speedy46

1. The problem statement, all variables and given/known data

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.

2. Relevant 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

3. 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.

2. Jan 21, 2009

### Q_Goest

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. Jan 22, 2009

### speedy46

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. Jan 22, 2009

### nvn

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. Jun 25, 2009

### speedy46

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

6. Jun 25, 2009

### Redbelly98

Staff Emeritus
9000-89000 is not 600
Looks like you typed something wrong, but it's not obvious where the mistake is.

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. Jun 26, 2009

### speedy46

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

8. Jun 26, 2009

### Redbelly98

Staff Emeritus

Things got a little sloppy here, but you probably just copied down things differently from where you worked this out on paper:
Should be V^2 = u^2 + 2×a×s,
but V=49.24 m/s is correct.