Tricky Physics Question regarding Dynamite!?

Question

Dynamite! A demolition crew uses dynamite to blow an old building apart. Debris from the explosion flies off in all directions, and is later found at distances up to a distance x from the explosion.

Find the maximum speed at which debris was blown outward by the explosion. Neglect air resistance.

My answer was :

L / sqrt g/2h

but it says im off by a multiplicative factor! HELP!

Answer 1

Measure the height from the ground to the bridge part in question. The work out how long it would take the piece to fall in a straight line down (9 .2 meters per second squared). The divide X by this number. So if it is 9.2 meters high and the debris is at 9.2 meters, it was traveling at 9.2 meters per second. If it was at a distance of 18.4 meters, it was traveling at 18.4 meters per second. If the height is greater, then the speed will be reduced because of the increased time taken to reach the ground - but you get the principle.

Answer 2

In order to provide any meaningful answer, one would need to know the height of the building. But, for the sake of argument, let's assume that all of the material in the building originated from the single detonation point (sort of like a mini big bang!). In that case, this is a simple projectile motion problem -- the material moves with constant x velocity, and y velocity influenced by gravity. One can solve this type of problem to find that the maximum distance is achieved by an initial angle of 45 deg. Normally one knows the initial velocity and is asked to find the distance, but your problem poses that the distance is known, and asks to solve for the initial velocity. Pretty much the same problem.

x = v_0*cos(45) *t

v_y = v_0 * cos(45) - a*t

Solving for v_y = 0 gives t = (0.5*v_0)/(9.8)

This is the time at which the debris reaches its maximum height and begins falling back to earth. The time at which it reaches earth is twice this time, or t_f = v_0/9.8

Now, x_f = 0.5*v_0*t_f, or v_0 = 2*x_f/t_f = 2*x_f*9.8/v_0

v_0^2 = 2*x_f*9.8

v_0 = sqrt(2*x_f*9.8)

Answer 3

The only factor limiting the velocity of the material is the speed of light.

Thanks for playing.

Answer 4

the problem doesn't have enough data.........if u at least knew the dynamites quantity or it's blast power