Magnetic Levitation Coaster Simulation and Slide Speed

Problem Statement

A new amusement park attraction is being designed: a "linear coaster" that slides down a straight slope, with magnetic levitation technology eliminating all friction between the car and the track.

Air resistance is negligible. It is theoretically known that the acceleration $a$a (rate of speed increase per second) of the car sliding down is proportional to the slope height $h$h and inversely proportional to the slope length $L$L. That is, with some unknown proportionality constant $k$k:

$$a = k \times \frac{h}{L}$$a=k×Lh​

The design team performed a preliminary test using computer simulation.

A test slope of length $L_0$L0​ and height $h_0$h0​ was built in the simulation space, and the car was released from rest at the top. The measured acceleration was $a_0$a0​.

Based on this result, a full-scale slope of length $L_1$L1​ and height $h_1$h1​ was designed. When the car is released from rest at the top of the full-scale slope, find the speed $v$v of the car at time $T$T after release.

Constraints

• $L_0 = 5.0 \ \mathrm{m}$L0​=5.0 m
• $h_0 = 2.0 \ \mathrm{m}$h0​=2.0 m
• $a_0 = 3.92 \ \mathrm{m/s^2}$a0​=3.92 m/s2
• $L_1 = 50.0 \ \mathrm{m}$L1​=50.0 m
• $h_1 = 15.0 \ \mathrm{m}$h1​=15.0 m
• $T = 4.0 \ \mathrm{s}$T=4.0 s

Input Format

Find the speed $v \ [\mathrm{m/s}]$v [m/s] and give the answer as a positive integer equal to the value multiplied by $100$100.