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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

Antlion larvae lie in wait for prey at the bottom of a conical pit about 5.0 cm deep and 3.8 cm in radius. When a small insect ventures into the pit, it slides to the bottom and is seized by the antlion. If the prey attempts to escape, the antlion rapidly launches grains of sand at the prey, either knocking it down or causing a small avalanche that returns the prey to the bottom of the pit. Suppose an antlion launches grains of sand at an angle of 72° above the horizon. Find the launch speed v0 required to hit a target at the top of the pit, 5.0 cm above and 3.8 cm to the right of the antlion.

To determine
The launch speed required to hit a target at the top of the pit.

Explanation

The x component of the displacement of sand grains is,

Δx=(v0cosθ)t

Here,

v0 is the initial velocity

θ is the launch angle

t is the time taken

t=Δxv0cosθ

The y component of the displacement of sand grains is,

Δy=(v0sinθ)t12gt2

Here,

g is the acceleration due to gravity

Substituting t=Δxv0cosθ ,

Δy=(v0sinθ)(Δxv0cosθ)12g(Δxv0cosθ)2=Δxtanθ12g(Δxv0cos

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