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kow [346]
3 years ago
7

A jet plane has a takeoff speed of vto = 75 m/s and can move along the runway at an average acceleration of 1.3 m/s2. If the len

gth of the runway is 2.5 km, will the plane be able to use this runway safely?

Mathematics
2 answers:
Yuliya22 [10]3 years ago
8 0

If the length of the runway is 2.5 km, then the plane will be able to use this runway safely.

<h3>Further explanation</h3>

These are the formulas that we have to remember before solving the problem.

Speed is the rate of change of distance.

\large { \boxed {v = \frac{d}{t}}}

<em>v = speed ( m/s )</em>

<em>d = distance ( m )</em>

<em>t = time ( s )</em>

Acceleration is the rate of change of velocity.

\large { \boxed {a = \frac{\Delta v}{t}}}

<em>a = acceleration ( m/s² )</em>

<em>Δv = change in speed ( m/s )</em>

<em>t = time ( s )</em>

Let us now tackle the problem!

<u>Given:</u>

Initial speed = u = 0 m/s

Final speed = v = 75 m/s

Average acceleration = a = 1.3 m/s²

<u>Unknown:</u>

Distance = d = ?

<u>Solution:</u>

v ^ 2 = u ^ 2 + 2 a d

75 ^ 2 = 0 ^ 2 + 2 ( 1.3 ) d

5625 = (2.6) d

d = 5625 \div 2.6

d \approx 2200 ~ m

\large {\boxed {d \approx 2.2 ~ km} }

The distance needed by the aircraft from a standstill to reach speeds of 75 m/s is around 2.2 km. The aircraft will be safe using the runway because the length of the runway ( 2.5 km ) is greater than the required distance ( 2.2 km ).

<h3>Learn more</h3>
  • Velocity of A Runner : brainly.com/question/3813437
  • Kinetic Energy : brainly.com/question/692781
  • Acceleration : brainly.com/question/2283922

<h3>Answer details</h3>

Grade: Middle School

Subject: Physics

Chapter: Kinematics

Keywords: Speed , Distance , Acceleration , Time , Velocity , Jet , Plane , TakeOff , Runway

pishuonlain [190]3 years ago
6 0
Initial velocity of the plane is Vo = 0.
acceleration a = 1.3 m/s2
total distance = 2.5 km = 2500m

time taken to reach 2.5 km with 1.3m/s^2 acceleration = t
S = Vo t + 0.5 a t^2
2500 = 0 + (0.5*1.3* t^2)
t^2 = 3846.15
t = 62 s

the maximum velocity plan can reach within 62 s is Vt
Vt = Vo + a t
Vt = 0 + (1.3*62)
Vt = 80.6 m/s

Since 80.6 m/s is greater than 75 m/s, plane can use this runway to takeoff with required speed.
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