Posted by **Sarah** on Sunday, June 7, 2009 at 9:53pm.

A markman fires a .22 caliber rifle horizontally at a target the bullet has a muzzle velocity with magnitude 750 ft/s. How much does the bullet drop in flight if the target is (a) 50.0 yd away and (b) 150.0 yd away?

for this question i was given the equation

S= ut + at^2/2

I don't know what numbers I should put where all i know is that a = -9.8 and u = 750 but the answer for the question is .64 how do they get this

- Physics -
**MathMate**, Sunday, June 7, 2009 at 10:43pm
Sorry Sarah if the previous explanation was not clear.

Since he shoots horizontally, the drop starts the moment the bullet leaves the rifle, at the rate of g (acceleration due to gravity).

For (a) and (b), calculate the time t the bullet is in the air using the horizontal speed, then calculate drop using

S=ut+at^2/2

where a=-g, and u the muzzle velocity.

The formula for S (distance) applies independently to horizontal and vertical directions.

u=initial velocity

a=acceleration

t=time

For part (a),

Horizontal direction:

time to reach 50 **yards** is the distance divided by the muzzle velocity. There is no acceleration (a=0) and air resistance is neglected.

S=ut + a t^{2}/2

50*3 = 750 * t + 0

Thus

t=50 yards * 3 ft/yd / 750 ft/s

=0.2 s.

Vertical direction:

u=initial vertical velocity = 0 (bullet was shot horizontally)

a=-g = -32.2 ft/s/s

S = 0*t + a t^{2}/2

= 0 + (-32.2)0.2^{2}/2 ft.

= 0 + (-32.2)* 0.04 /2 ft.

= 0.644 ft.

I am sure you can do part (b) along the same lines. Post your answer if you want it checked.

- Physics -
**Sarah**, Monday, June 8, 2009 at 1:35pm
how did you .644 to not be a negative ???

- Physics -
**MathMate**, Monday, June 8, 2009 at 1:50pm
Correct, it should be negative, since the bullet drops downwards.

Thank you.

- Physics -
**Sarah**, Monday, June 8, 2009 at 1:54pm
well in the book it says its not negative either

- Physics -
**MathMate**, Monday, June 8, 2009 at 1:59pm
You have the correct mathematical answer of -0.644.

But the question asks

"How much does the bullet **drop** in flight ..."

so the direction is implied, so the negative is not required.

You only have to translate the mathematical answer to a human answer.

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