To take off from the ground, an airplhttp://www.cramster.com/askane must reach a

Question

To take off from the ground, an airplhttp://www.cramster.com/askane must reach a sufficiently high speed. The velocity required for the takeoff, the takeoff velocity, depends on several factors, including the weight of the aircraft and the wind velocity.

A plane accelerates from rest at a constant rate of 5.00 m/s^2 along a runway that is 1800 m long. Assume that the plane reaches the required takeoff velocity at the end of the runway. What is the time t_{TO} needed to take off?

t TO = s

What is the distance d_first traveled by the plane in the first second of its run?
d first= m

What is the distance d_last traveled by the plane in the last second before taking off?
d last= m

Explanation / Answer

We know acceleration and the x distance, and assume that initial velocity is 0. Therefore, we can use this equation:

x=x0+v0t+1/2at^2
1800=0+0+1/2*5*t^2

Solve for t to get: 26.83 s

In the first second, we know that initial velocity is 0, acceleration is 5. We can use the same equation to solve for distance:

x=0+0+1/2*5*(1)^2 = 2.5 m

To find the distance the plane traveled in the last second, we can find the distance it traveled in the seconds leading up to that, then subtract that value from 1800. We know that time was 26.83 seconds, so we will solve for t=25.83 seconds. We can use the same equation we have been using:

x=0+0+1/2*5*(25.83)^2 = 1668.34 m

1800 m - 1668.34 m = 131.664 m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.