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Chapter 12: Problem 147

The jet plane is traveling with a speed of \(120 \mathrm{~m} / \mathrm{s}\) which is decreasing at \(40 \mathrm{~m} / \mathrm{s}^{2}\) when it reaches point \(A\). Determine the magnitude of its acceleration when it is at this point. Also, specify the direction of flight, measured from the \(x\) axis.

Short Answer

Expert verified
The magnitude of the acceleration of the jet plane when it reaches point A is \(40 \mathrm{~m} / \mathrm{s}^{2}\) and the direction of flight is along the x-axis.

Step by step solution

01

Determine the magnitude of the acceleration

Since the plane is slowing down, its acceleration is negative. The rate of decrease in speed or deceleration is given as \(40 \mathrm{~m} / \mathrm{s}^{2}\). So, the magnitude of deceleration is equivalent to the magnitude of acceleration, which is \(40 \mathrm{~m} / \mathrm{s}^{2}\). Because the direction of acceleration is opposite to the velocity.
02

Determine the direction of flight

The direction of flight is along the path of velocity, which is the line of motion of the jet. The direction of acceleration and velocity are opposite as the jet is decelerating. If we assume the direction of velocity as the positive x-direction, the direction of acceleration will be negative x-direction, which is 180 degrees away from the x-axis.

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Most popular questions from this chapter

Cars \(A\) and \(B\) are traveling around the circular race track. At the instant shown, \(A\) has a speed of \(60 \mathrm{ft} / \mathrm{s}\) and is increasing its speed at the rate of \(15 \mathrm{ft} / \mathrm{s}^{2}\) until it travels for a distance of \(100 \pi \mathrm{ft}\), after which it maintains a constant speed. Car \(B\) has a speed of \(120 \mathrm{ft} / \mathrm{s}\) and is decreasing its speed at \(15 \mathrm{ft} / \mathrm{s}^{2}\) until it travels a distance of \(65 \pi\) ft, after which it maintains a constant speed. Determine the time when they come side by side.

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