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3 years ago

1. How fast must a truck travel to stay beneath an airplane that is moving

Physics

1 answer:

Xelga [282]3 years ago

8 0

Answer:

The truck must travel by 95.16 km/h to stay beneath the airplane

Explanation:

Lets explain how to solve the problem

How fast must a truck travel to stay beneath an airplane that is moving

105 km/h at an angle of 25° to the ground

The truck moves a long the horizontal ground

The airplane moves 105 km/h at an angle 25° to the ground

The truck must moves with velocity equal the horizontal component

of the velocity of the airplane to stay beneath the airplane

The angle between the line represented the velocity of the airplane

and the ground is 25°

→ The horizontal component of the velocity = v cos(25)

→ The velocity of the airplane is 105 km/h

→ The horizontal component = 105 cos(25) = 95.16 km/h

The velocity of the truck = the horizontal component of the airplane

The truck must travel by 95.16 km/h to stay beneath the airplane

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Explanation:

From the question we are told that

The acceleration is $a = \frac{c}{s}\ m/s^2$

The initial position of the projectile is s= 1.5m

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Generally $time = \frac{ds}{dv}$

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$a = v \frac{dv}{ds}$

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integrating both sides

$\int\limits^a_b vdv = \int\limits^c_d \frac{c}{s} ds$

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$\int\limits^{200}_{0} vdv = \int\limits^{3}_{1.5} \frac{c}{s} ds$

$[\frac{v^2}{2} ] \left | 200} \atop {0}} \right. = c [ln s]\left | 3} \atop {1.5}} \right.$

$\frac{200^2}{2} = c ln[\frac{3}{1.5} ]$

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