KinexiaLEARN PHYSICS

SUVAT v² Equation — Ski Jump Inrun (Worked Example)

Hard
Problem

A ski jumper enters the inrun at 12 m/s and accelerates uniformly at 4 m/s² over the 50 m ramp. What is her speed at takeoff?

Given

  • u = 12 m/s

  • a = 4 m/s²

  • s = 50 m

Find

The takeoff speed v.

Principle

With distance known but time unknown, v² = u² + 2as is the efficient choice — one equation, one unknown.

Formula

Solution

  1. Write the equation: v2=u2+2asv^2 = u^2 + 2as

  2. Substitute: v2=122+2(4)(50)v^2 = 12^2 + 2(4)(50)

  3. Calculate: v2=144+400=544v^2 = 144 + 400 = 544

  4. Square root: v=544=23.3 m/sv = \sqrt{544} = 23.3\ \mathrm{m/s}

23.3 m/s

Unit check

√((m/s)² + m/s²·m) = m/s — a speed, correct.

What this means physically

23.3 m/s (≈84 km/h) at the lip — nearly double the entry speed. That extra kinetic energy becomes the flight distance that wins competitions.

Common mistake

Adding u + 2as without squaring u first. The equation needs u² — compute each term in the right order.