FYKOS Year 31 Series 6 Problem 4 — dimensional analysis · FYKOS 31 #31.6.4

Physics · mechanics

Problem

Matej was making a gun and wanted to measure what is the speed of the projectiles leaving the barrel. Unfortunately, he doesn't have any other measuring device, than a ruler. However, he found a block that is made half from steel half from wood. He lays it down at the edge of the table (of height 100 cm100 \mathrm{cm} and length 200 cm200 \mathrm{cm}), and shoots at it horizontally. With the steel part of the block facing the gun, the bullet bounces off perfectly elastically and lands 50 cm50 \mathrm{cm} from the edge of the table. The block slides 5 cm5 \mathrm{cm} on the table. Then Matej turns around the block and shoots into the wooden side. This time the bullet stays in the block and the block slides only 4 cm4 \mathrm{cm}. Help Matej with calculating the speed of the bullet. It might be also helpful to know, that when Matej lifts one edge of the table by at least 20 cm20 \mathrm{cm}, the moving block won't stop sliding.

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