# Skip bombing problem

wangliqin_loc

A fast plane approaches the dam in level flight at low altitude h1, with speed v. A bomb is released which skips off the water and bounces up against the dam, striking it at a height h2 above the water. Given the speed of the plane, and assuming that the bomb loses no speed when it bounces off the water(not very realistic), and that the bomb bounces off the water at the same angle at which it hits, how far from the dam should the bomb be released? Solve for this distance x in terms of v, h1, h2, and g

Mentor
not very realistic? this is the famous dambusters event of WW2 where a cylindrical bomb was spun up and then dropped a fixed distance from the target dam. It skipped right up to the wall and then sunk whereupon it exploded flooding a large part of the countryside in Germany.

http://en.wikipedia.org/wiki/Dambusters_Raid

also NOVA did a show where some scientists tried to reproduce the design work on the bomb.

Lastly, we need to see some work before we can help with your problem.

wangliqin_loc
ok, so I can figure myself the distance from the release of the boom until it touches the water, but I'm stuck at finding the distance from the bounce of the bomb to the dam.

voko
The entire trajectory consists of two parts. Before the bounce and after. The duration of the first one is determined by the release height. The duration of the second is determined by the upward speed at the bounce (which is a function of the release height) and the target height. These two durations together times the release speed is the distance sought.

Staff Emeritus
Homework Helper

azizlwl
ok, so I can figure myself the distance from the release of the boom until it touches the water, but I'm stuck at finding the distance from the bounce of the bomb to the dam.

For the 2nd. part use kinematic and conservation of enery equations.

You should know the velocity when it touches the water and bounce equally and the velocity when it hits the dam by using conservation of energy equation. Horizontal KE remain constant.Energy is scalar.
The acceleration throught the flight is constant.

Homework Helper

A fast plane approaches the dam in level flight at low altitude h1, with speed v. A bomb is released which skips off the water and bounces up against the dam, striking it at a height h2 above the water. Given the speed of the plane, and assuming that the bomb loses no speed when it bounces off the water(not very realistic), and that the bomb bounces off the water at the same angle at which it hits, how far from the dam should the bomb be released? Solve for this distance x in terms of v, h1, h2, and g

The assumptions in red above means that after an appropriate amount of time, the bomb would be back up at plane level!!

You said you could calculate the time and distance involved if falling the height h1.
It should be a similar calculation to work out time and distance to regain h2.

similar problem.

A perfect rubber ball is dropped from a height of 20m, falls to the ground and instantly does a perfect bounce back [same speed after as before],
taking g = 10 for simplicity - how long does the ball take to reach the ground? and how long does it take to get back to a height of 5m?