Question

a bullet has a speed of 350 m/s as it leaves a rifle it is fired horizontally from a cliff 6.4m above a lake how far does the bullet travel before striking the water

Answer 1

We have a 2-dimensional problem with constant acceleration (acceleration due to gravity).

This is a projectilemotionproblem.

The figure is as shown and the coordinate system selected is drawn.

The origin is placed at the bullet's location at time t=0.

Hence the initial conditions for the problem are:x(t=0) = xo= 0 ; y(t=0) = yo= 0vx(t=0) = vox= 350 m/s; vy(t=0) = v oy = 0 x y 6.4 m v o a Since the only force acting is gravity (downward = + y direction), we have: a x = 0; ay= + g = + 9.8 m/sec2.

The general solutionsfor the constant acceleration problem in two dimensions are:x(t) = (1/2) axt2+ voxt + xoy(t) = (1/2) a y t 2 + v oy t + y o v x (t) = a x t + v ox v y (t) = a y t + v oy Inserting the values of acceleration and the initial conditions gives us the specific equations (applicable to this one particular problem). x(t) = (350) t y(t) = (1/2)(9.8) t 2 v x = 350 m/s v y (t) = 9.8 t Let t' be the time when the bullet hits the lake. We then know that: y(t') = + 6.4 m. Thus: y(t') = + 6.4 = + 4.9 t' 2  t' = 1.143 sec.

The horizontal (x) position of the bullet at this time is then: x(t') = (350)(1.143) = 400 m.