Question

Problem 6. Consider two aircraft present on the same runway, and moving in opposite directions, as shown in the figure. The two aircraft are initially 5 km away from each other. The first aircraft, labeled 1, is taxiing at low speed (about 40 km/h). The other aircraft, labeled 2, is taking off starting from 0 initial speed, accelerating at constant acceleration equal to 0.5 m/s² (30 points) 1. Write an expression for the distance between the two aircraft as a function of time. 2. Let O be the point where the two airplanes collide. What is the location of the point O? (Assume each aircraft is a particle, ahem ahem...) 3. Compute analytical formulas for the speeds and accelerations of both aircraft in the reference frame O and the basis $(\hat{i}; \hat{j})$ as shown. What are the values of these speeds and accelerations at the time of collision? 4. Repeat Question 3, but use the reference frame O1 and the basis $(\hat{i}_1; \hat{j}_1)$. Repeat the same question with the reference frame O2 and the basis $(\hat{i}_2; \hat{j}_2)$. 5. Compute analytical formulas for the speed and acceleration of aircraft 2 in the reference frame O1 of aircraft 1, but using the basis $(\hat{i}; \hat{j})$. What are the speed and accelerations at the time of collision?

          Problem 6.
Consider two aircraft present on the same runway, and moving in opposite directions, as shown in
the figure. The two aircraft are initially 5 km away from each other. The first aircraft, labeled 1,
is taxiing at low speed (about 40 km/h). The other aircraft, labeled 2, is taking off starting from
0 initial speed, accelerating at constant acceleration equal to 0.5 m/s² (30 points)
1. Write an expression for the distance between the two aircraft as a function of time.
2. Let O be the point where the two airplanes collide. What is the location of the point O?
(Assume each aircraft is a particle, ahem ahem...)
3. Compute analytical formulas for the speeds and accelerations of both aircraft in the reference
frame O and the basis $(\hat{i}; \hat{j})$ as shown. What are the values of these speeds and accelerations
at the time of collision?
4. Repeat Question 3, but use the reference frame O1 and the basis $(\hat{i}_1; \hat{j}_1)$. Repeat the same
question with the reference frame O2 and the basis $(\hat{i}_2; \hat{j}_2)$.
5. Compute analytical formulas for the speed and acceleration of aircraft 2 in the reference frame
O1 of aircraft 1, but using the basis $(\hat{i}; \hat{j})$. What are the speed and accelerations at the time
of collision?

Problem 6.
Consider two aircraft present on the same runway, and moving in opposite directions, as shown in
the figure. The two aircraft are initially 5 km away from each other. The first aircraft, labeled 1,
is taxiing at low speed (about 40 km/h). The other aircraft, labeled 2, is taking off starting from
0 initial speed, accelerating at constant acceleration equal to 0.5 m/s² (30 points)
1. Write an expression for the distance between the two aircraft as a function of time.
2. Let O be the point where the two airplanes collide. What is the location of the point O?
(Assume each aircraft is a particle, ahem ahem...)
3. Compute analytical formulas for the speeds and accelerations of both aircraft in the reference
frame O and the basis (î; ĵ) as shown. What are the values of these speeds and accelerations
at the time of collision?
4. Repeat Question 3, but use the reference frame O1 and the basis (î1; ĵ1). Repeat the same
question with the reference frame O2 and the basis (î2; ĵ2).
5. Compute analytical formulas for the speed and acceleration of aircraft 2 in the reference frame
O1 of aircraft 1, but using the basis (î; ĵ). What are the speed and accelerations at the time
of collision?

Added by Darrell J.

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