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# Find the bullet's range?

A bullet was fired horizontally from the top of a 150 m tall tower at 280 m/s. Find the bullet's range and time of flight. Determine also its speed on impact with the ground below.

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Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
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We have the kinematic equations

Δx = v0t,  Δy = -½gt²

With Δy = -150 m, solving the second equation for t gives us

t = √(2(150)/9.8) s = 5.53 s.

This is the flight time. Plug it into the first equation to get the range:

Δx =280 (5.53) m = 1550 m.

To find the speed on impact we need the two components of the final velocity. The velocity's x-component doesn't change, so

vx = v0= 280 m/s.

For the y-component we have the kinematic equation

vy=-gt = -9.8 (5.53) m/s = -54.2 m/s

The final speed is the magnitude of the final velocity. Use the Pythagorean theorem to find

v = √(vx²+vy²) = √(280²+(-54.2)²) = 285 m/s.