Question

How fast must a truck travel to stay beneath an airplane that is moving 125 km/h at an angle of 35º to the ground?

Answer 1

v = 102.4 km/h

Explanation:

Given:-

- The speed of the airplane, u = 125 km/h

- the angle the airplane makes with the ground, θ = 35°

Find:-

How fast must a truck travel to stay beneath an airplane?

Solution:-

- For the truck to be beneath the airplane at all times it must travel with s projection of airplane speed onto the ground.

- We can determine the projected speed of the airplane by making a velocity (right angle triangle).

- The Hypotenuse will denote the speed of the airplane which is at angle of θ from the truck travelling on the ground with speed v.

- Using trigonometric ratios we can determine the speed v of the truck.

v = u*cos ( θ )

v = (125 km/h) * cos ( 35° )

v = 102.4 km/h

- The truck must travel at the speed of 102.4 km/h relative to ground to be directly beneath the airplane.

Answer 2

The horizontal speed of the truck is 102.39 km/hr.

Explanation:

Given that,

Speed of airplane = 125 km/h

Angle = 35°

We need to calculate the horizontal speed

Using formula of horizontal speed

`u_(x)=u\cos\theta`

Where, u = speed

Put the value into the formula

`u_(x)=125*\cos35^(\circ)`

`u_(x)=102.39\ km/hr`

Hence, The horizontal speed of the truck is 102.39 km/hr.