A pistol that fires a signal flare gives it an initial velocity (muzzle velocity

Question

A pistol that fires a signal flare gives it an initial velocity (muzzle velocity) of 134 m/s at an angle of 58.9^circ 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 in meters.

Find the distance from its firing point to its landing point if it is fired on the level salt flats of Utah in meters.

Find the flare's maximum height if it is fired over the flat Sea of Tranquility on the Moon, where g = 1.67 m/s^2. Answer in meters

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 = 1.67 m/s^2. Answer in meters.

Explanation / Answer

a) Max height

vy=134 m/s * sin 58.9 = 114.7 m/s

v2=vi2+2a*y

At the top of its arc v=0

0=114.72-2*9.8*y

y max (earth) = 671.7 meters

On the moon, same thing just change the g value

0=114.72 - 2*1.67y

y max (moon) = 3938.95 meters

b) Distance

vx=134*cos58.9 = 69.2 m/s, you already know vy= 114.7 m/s from part A

Time it takes to fall: v=vi+at. Since air resistance is ignored the final vyfinal = -vyi =-114.7 m/s

-114.7 = 114.7 - 9.8t - t=23.41s (earth)

-114.7 = 114.7 - 1.67t - t=137.37s (moon)

Distance travelled: x = xi + vt

Earth: X = 69.2*23.41 = 1620m

Moon X = 69.2*137.37 = 9506m

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