An airplane travelling north at 400 m/s is accelerated due east at a rate of 50m/s^2 for 6 seconds. If the effects of air resistance and gravity are ignored, what is the final speed of the plane?
My working:
v=vo+at
where a=50m/s
Vo = 400 m/s
t = 6s
thus: Vo=400+50(6)
=700m/s
But the correct answer is 500 m/s what am i doing wrong?
The two numbers cannot be added directly, because they are 90o out of phase:
V = 300 + 400i.
You only want the magnitude:
V = sqrt(300^2+400^2) = 500 m/s.
Well, it seems the airplane got a bit carried away with the acceleration! Let's break it down and see where things went sideways.
First, we have the initial velocity of the plane, which is 400 m/s. Then comes the acceleration. However, this acceleration is acting perpendicular to the direction of motion, so it won't affect the speed directly. It'll only change the plane's direction.
In other words, while the plane will change course and head east (maybe for some impromptu sightseeing), it won't increase or decrease its speed.
So, the final speed of the plane will remain the same as the initial speed, which is 400 m/s. Therefore, the correct answer is indeed 400 m/s, and we can let the airplane kick back and relax during its little detour. Safe travels!
Your initial approach is correct, but there is a small error in your calculation. Let's go through the problem step by step to identify the mistake:
Given:
- Initial velocity (Vo) = 400 m/s (north)
- Acceleration (a) = 50 m/s^2 (east)
- Time (t) = 6 seconds
To find the final velocity (v), we can use the equation:
v = Vo + at
Substituting the given values:
v = 400 + 50(6)
v = 400 + 300
v = 700 m/s (east)
From your calculations, you obtained the same intermediate result correctly.
Now, since the airplane is initially moving north, any acceleration applied to the east would not affect the magnitude of its velocity in the north-south direction. This means the final speed or magnitude of the velocity will be the same as the initial speed, which was 400 m/s.
Hence, the correct final speed of the airplane is indeed 400 m/s, not 500 m/s as you mentioned.
Please let me know if you need any further clarification.
Your equation v = vo + at is correct, but you made a mistake in plugging in the values.
Let's break down the calculation step by step:
vo = 400 m/s (initial speed)
a = 50 m/s^2 (acceleration)
t = 6 s (time)
Using the equation v = vo + at:
v = 400 m/s + 50 m/s^2 * 6 s
Now, let's evaluate the equation:
v = 400 m/s + 300 m/s
Adding the terms:
v = 700 m/s
So, your calculation is correct, and the final speed of the plane is indeed 700 m/s, not 500 m/s.
It seems there might be an error in the provided correct answer. Double-check the solution or consult the source you obtained the answer from.