A pistol that fires a signal flare gives it an initial velocity (muzzle velocity
ID: 1884083 • Letter: A
Question
A pistol that fires a signal flare gives it an initial velocity (muzzle velocity) of 179 m/s at an angle of 65.0 above the horizontal. You can ignore air resistance.
Find the flare's maximum height if it is fired on the level salt flats of Utah.
Find the distance from its firing point to its landing point if it is fired on the level salt flats of Utah.
Find the flare's maximum height if it is fired over the flat Sea of Tranquility on the Moon, where g=1.62m/s2.
Find the distance from its firing point to its landing point if it is fired over the flat Sea of Tranquility on the Moon, where g=1.62m/s2.
Explanation / Answer
PROJECTILE
along vertical
______________
initial velocity v0y = v*sintheta = 179*sin65
acceleration ay = -g = -9.8 m/s^2
initial position y0 = 0
final position y = h
final velocity vy = 0 ( at maimum height )
from equation of motion
vy^2 - voy^2 = 2*ay*(y-yo)
0^2 - (179*sin65)^2 = -2*9.8*(h-0)
h = 1343 m <<<---------answer
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after the flare lands displacement y = 0
along vertical
from equation of motion
y = voy*t + (1/2)*ay*t^2
0 = (179*sin65*t) - (1/2)*9.8*t^2
t = 33.1 s
along horizontal
________________
initial velocity v0x = v*costheta = 179*cos65
acceleration ax = 0
initial position = xo = 0
final position = x m
from equation of motion
x - x0 = v0x*T + 0.5*ax*t^2
x = 179*cos65*33.1
x = 2504 m <<<---------answer
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along vertical
______________
initial velocity v0y = v*sintheta = 179*sin65
acceleration ay = -g = -9.8 m/s^2
initial position y0 = 0
final position y = h
final velocity vy = 0 ( at maimum height )
from equation of motion
vy^2 - voy^2 = 2*ay*(y-yo)
0^2 - (179*sin65)^2 = -2*1.62*(h-0)
h = 8123 m <<<---------answer
----------------------------------------
after the flare lands displacement y = 0
along vertical
from equation of motion
y = voy*t + (1/2)*ay*t^2
0 = (179*sin65*t) - (1/2)*1.62*t^2
t = 200.3 s
along horizontal
________________
initial velocity v0x = v*costheta = 179*cos65
acceleration ax = 0
initial position = xo = 0
final position = x m
from equation of motion
x - x0 = v0x*T + 0.5*ax*t^2
x = 179*cos65*200.3
x = 15152 m <<<---------answer
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