Question

---O (11011 0 JOUUDIO m w your nand)? t= sec = _min (keep 2 significant digits in your answers to this problem). Long range big guns can shoot a shell at the muzzle speed about 1.50 km/sec. How far can this shell go if shot directly up? h= km= miles. How long would it be in the air? t = sec = min :) If there were no air drag, at what speed would raindrops hit the ground when they fall from a cloud at a typical 5.00 km altitude? V = m/s = mph. Some hailstone falls from 15.0 km high thunderstorm clouds and could accumulate mass about 0.5 kg over such long fall. What would be the speed of that hailstone at the absence of air drag? V=_ _m/s = _mph. Is this dangerous (to be hit by it)? _ To estimate that, you, may want to calculate the kinetic energy K = mv-/2 = _Joules of such ice piece and compare it with the energy needed to do significant harm or even cause death to a human to be about 100 Joules.

Answer 1

3) Long range run v = 1.5 km/s = 1500 m/s

$h=\frac{v^2}{2g}=\frac{1500^2}{(2\times 9.8)}=114796\,m = 376627\,\,ft = 114.8 \,km=71.3\,miles$

the time taken for the bullet to return(time it remains in air) is

$t = 2v/g=2\times 1500/9.8=306.1\,s=306.1/60 \,min = 5.1\,min$

4) h = 5 km = 5000 m

$v=\sqrt{2gh}=\sqrt{2\times 9.8\times 5000}=313.05\,m/s=313.05\times 2.24\,mph$

$v=700\,mph$

for hailstones, h = 15 km = 15000 m

$v=\sqrt{2gh}=\sqrt{2\times 9.8\times 15000}=542.2\,m/s=542.2\times 2.24\,mph$

$v=1213\,mph$

Kinetic energy is

$K=mv^2/2=0.5\times 542.2^2/2=73500\,J$

Since this is much greater than 100 J it is dangerous to get hit by it