Projectile

{
  "angleDeg": 30,
  "asOf": "2026-10-11T08:56:13.534Z",
  "degraded": false,
  "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
  "flightTimeS": 2.7744964,
  "gravity": 9.80665,
  "horizontalSpeed": 17.320508,
  "impactAngleBelowHorizontalDeg": 44.814165,
  "impactSpeed": 24.415835,
  "initialVerticalSpeed": 10,
  "launchHeight": 10,
  "maxHeightM": 15.098581,
  "maxRangeAngleForGroundLaunchDeg": 45,
  "notChecked": [
    "air drag, which shortens real ranges a lot for fast or light objects",
    "wind, spin, Earth's rotation and curvature (only valid for ranges small against the planet's radius)",
    "…1 more"
  ],
  "rangeM": 48.055688,
  "reasons": [
    "t = (v sin(a) + sqrt(v^2 sin^2(a) + 2 g h)) / g; range = v cos(a) t; max height = h + v^2 sin^2(a) / 2g. Drag is ignored."
  ],
  "source": "computed locally",
  "speed": 20,
  "summary": "Launch 20 m/s at 30 degrees from 10 m with g = 9.80665: flight time 2.774 s, range 48.06 m, maximum height 15.1 m, hits at 24.42 m/s.",
  "timeToApexS": 1.0197162,
  "verdict": "COMPUTED"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://physics-calc.x402tookit.com/projectile?angleDeg=30&height=10&speed=20'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://physics-calc.x402tookit.com/projectile?angleDeg=30&height=10&speed=20' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

// npm i @x402/fetch @x402/evm viem
import { wrapFetchWithPayment, x402Client } from "@x402/fetch";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Fphysics-calc.x402tookit.com%2Fprojectile
const res = await pay("https://physics-calc.x402tookit.com/projectile?angleDeg=30&height=10&speed=20");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://physics-calc.x402tookit.com/projectile?angleDeg=30&height=10&speed=20")
    print(res.status_code, res.text)