Question 10

An airplane traveling north at 400 m/s is accelerated due east at a rate of 50 m/s2 for 6 s. If the effects
of air resistance and gravity are ignored, what is the final speed of the plane?
1. 300 m/s
2. 400 m/s
3. 500 m/s
4. 700 m/s
5. 800 m/s

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To find the final speed of the plane, we need to calculate the net velocity of the plane after the acceleration of 50 m/s^2 for 6 seconds.

The first step is to find the change in velocity caused by the acceleration in the east direction. We can use the formula:

Change in velocity (Δv) = acceleration (a) × time (t)

Substituting the values given:

Δv = 50 m/s^2 × 6 s
= 300 m/s

Now, since the change in velocity is in the east direction, it does not directly affect the northward velocity of the plane. Therefore, the final speed of the plane can be given as:

Final speed = Initial speed + Change in velocity

The initial speed of the plane is given as 400 m/s, and the change in velocity is 300 m/s. Therefore:

Final speed = 400 m/s + 300 m/s
= 700 m/s

Therefore, the correct answer is option 4. 700 m/s.