Trex Calculator

T-Rex Obstacle Clearance Calculator

Ever wondered if your T-Rex in the popular offline game could actually clear that towering cactus or swooping pterodactyl? This calculator uses simplified physics to estimate a T-Rex's jump capabilities and determine if it can successfully clear obstacles based on its initial jump velocity and running speed.

Understanding the T-Rex Calculator

The "T-Rex Calculator" is inspired by the iconic Google Chrome offline game, where a pixelated T-Rex navigates a desert landscape, jumping over cacti and ducking under pterodactyls. While the game's physics are simplified, this calculator attempts to apply basic projectile motion principles to determine if a T-Rex, given certain physical parameters, could realistically clear an obstacle.

How It Works: The Physics Behind the Jump

A T-Rex's jump is a classic example of projectile motion. When the T-Rex pushes off the ground, it gains an initial vertical velocity. Gravity then acts upon it, slowing its upward movement until it momentarily stops at its peak height, before pulling it back down. Simultaneously, its running speed provides the horizontal component of its motion.

• Initial Vertical Jump Velocity: This is the speed at which the T-Rex leaves the ground in an upward direction. A higher initial velocity means a higher jump.
• T-Rex Running Speed: This is the constant horizontal speed the T-Rex maintains throughout its jump. This speed, combined with the time spent in the air, determines how far it travels horizontally.
• Obstacle Height: The vertical dimension of the obstacle (e.g., a tall cactus).
• Obstacle Width: The horizontal dimension or gap the T-Rex needs to cover to clear the obstacle.

The Formulas Used:

We use the following simplified physics formulas, assuming a constant gravitational acceleration (g) of 9.81 m/s²:

1. Maximum Jump Height (h_max): This is calculated using the formula: h_max = (Initial Vertical Jump Velocity)² / (2 * g). This tells us the highest point the T-Rex will reach.
2. Time in Air (t_air): The total time the T-Rex spends airborne is calculated as: t_air = (2 * Initial Vertical Jump Velocity) / g. This accounts for both the ascent and descent.
3. Horizontal Jump Distance (d_horizontal): This is determined by multiplying the T-Rex's running speed by the total time it spends in the air: d_horizontal = T-Rex Running Speed * t_air.

Interpreting the Results:

The calculator will provide the maximum height the T-Rex can achieve and the total horizontal distance it can cover during its jump. It then compares these values to the obstacle's height and width:

• If the T-Rex's maximum jump height is greater than or equal to the obstacle's height, AND its horizontal jump distance is greater than or equal to the obstacle's width, it is deemed to "Can clear!" the obstacle.
• Otherwise, it "Cannot clear!" the obstacle, indicating a potential collision in the game.

Realistic Examples:

Let's consider some realistic (for a game) scenarios:

• Scenario 1: Small Cactus
  • T-Rex Initial Vertical Jump Velocity: 4.0 m/s
  • T-Rex Running Speed: 7.0 m/s
  • Obstacle Height: 0.8 meters
  • Obstacle Width: 0.5 meters
  • Result: Max Jump Height ~0.82m, Horizontal Jump Distance ~5.71m. Likely "Can clear!"
• Scenario 2: Tall Cactus Cluster
  • T-Rex Initial Vertical Jump Velocity: 4.5 m/s
  • T-Rex Running Speed: 8.0 m/s
  • Obstacle Height: 1.5 meters
  • Obstacle Width: 1.0 meters
  • Result: Max Jump Height ~1.03m, Horizontal Jump Distance ~7.34m. In this case, the T-Rex might not jump high enough, resulting in "Cannot clear!"
• Scenario 3: Pterodactyl (requiring higher jump)
  • T-Rex Initial Vertical Jump Velocity: 5.5 m/s
  • T-Rex Running Speed: 9.0 m/s
  • Obstacle Height: 2.0 meters
  • Obstacle Width: 1.5 meters
  • Result: Max Jump Height ~1.54m, Horizontal Jump Distance ~10.1m. Still "Cannot clear!" due to insufficient height. The T-Rex would need a higher initial vertical velocity to clear a 2-meter obstacle.

Use this calculator to experiment with different values and see what it takes for your T-Rex to become an unstoppable obstacle-clearing machine!