A pilot flies horizontally at 1300 km/h, at height h ! 35 m above initially level ground. However, at time t ! 0, the pilot begins to fly over ground sloping upward at angle u ! 4.3° (Fig. 2-38). If the pilot does not change the airplane’s heading, at what time t does the plane strike the ground?

1 answer

Question:

A pilot flies horizontally at 1300 km/h, at height h ! 35 m above initially level ground. However, at time t ! 0, the pilot begins to fly over ground sloping upward at angle u ! 4.3° (Fig. 2-38). If the pilot does not change the airplane’s heading, at what time t does the plane strike the ground?

Answer:The pilot has only 1.3s before touching the ground.Explanation:This exercise the pilot flies horizontally and the ground rises slowly we can calculate the distance so that the ground is at the height of the plane, using trigonometry.
tan θ = y / x
x = y / tan θ
x = 35 / tan 4.3
x = 465.5 m
This is the distance that is needed for the ground with this inclination reaching the height of the plane. Now with the kinematic equations we can calculate the time it takes for the plane to travel this distance
Let's start with reducing the speed to SI units
Vx = 1300 km/h (1000m / 1km) (1h / 3600 s)
Vx = 361.1 m / s
Vx = x / t
t = x / Vx
t = 465.5 / 361.1
t = 1.3 s
The pilot has only 1.3s before touching the ground.

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