   Chapter 3, Problem 16P

Chapter
Section
Textbook Problem

An artillery shell is fired with an initial velocity of 300 m/s at 55.0° above the horizontal. To clear an avalanche, it explodes on a mountainside 42.0 s after firing. What are the x- and y-coordinates of the shell where it explodes, relative to its firing point?

To determine
The x and y components of the shell where it explodes, relative to its firing point.

Explanation

The horizontal component of the velocity of the projectile is,

v0x=v0cosθ

Substitute 300m/s for v0 and 55.0° for θ .

v0x=(300m/s)cos55.0°=172m/s

The vertical component of the velocity of the projectile is,

v0y=v0sinθ

Substitute 300m/s for v0 and 55.0° for θ .

v0y=(300m/s)sin55.0°=246m/s

For a projectile the components of acceleration are

ax=0m/s2ay=9.80m/s2

The x coordinate of the shell strikes the mountain is,

x=v0xt+12axt2

Substitute 172m/s for v0x , 42.0s for t and 0m/s2 for ax

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