Chapter 3, Problem 16P

### College Physics

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

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
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=v0cosÎ¸

Substitute 300â€‰m/s for v0 and 55.0Â° for Î¸ .

v0x=(300â€‰m/s)cos55.0Â°=172â€‰m/s

The vertical component of the velocity of the projectile is,

v0y=v0sinÎ¸

Substitute 300â€‰m/s for v0 and 55.0Â° for Î¸ .

v0y=(300â€‰m/s)sin55.0Â°=246â€‰m/s

For a projectile the components of acceleration are

ax=0â€‰m/s2ay=âˆ’9.80â€‰m/s2

The x coordinate of the shell strikes the mountain is,

x=v0xt+12axt2

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

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