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Chapter 2: Q74P (page 37)

A pilot flies horizontally at 1300km/h, at height h=35mabove initially level ground. However, at time t=0, the pilot begins to fly over ground sloping upward at angleθ=4.3°(Fig. 2-41). If the pilot does not change the airplane’s heading, at what time does the plane strike the ground?

Short Answer

Expert verified

The time t at which the plane strikes the ground is 1.29 s

Step by step solution

01

Given data

The speed of the plane is v=1300km/hat height h=35mabove the ground.

The angle sloping upward isθ=4.3°.

02

Relation between speed, distance, and time at constant acceleration

When acceleration is constant one can say that speed is the ratio of distance and time.

03

Calculation of distance using trigonometry

If the plane moves with velocity v=1300km/hcontinuously and the terrain continues its upward slope of 4.3°, then the plane will strike the ground after traveling a distance of

x=htan4.3=35mtan4.3=465.5m

So, the time of flight is,

t=xv=0.465km1300km/h=0.00036hr=1.29s≈1.3s

Therefore, at 1.3 s the plane will hit the ground.

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