Thrown up at 90 m/s: height and time

A stone is thrown straight up at 90 m/s (g = 10 m/s²). Find the maximum height it rises and the total time from the throw until it returns to the thrower's hand.

Step-by-step

1. h = v₀²/(2g) = 90²/(2×10) = 405
   The upward leg ends at speed 0, and v₀² = 2gh gives the maximum height
2. t = 2v₀/g = 2×90/10 = 18
   Rising and falling take equal times, so the total is 2 times the rise time

Why it works

Gravity alone acts on the stone, so its upward speed drops by 10 m/s each second until it is zero at the top; the fall then mirrors the rise, making the total time twice the rise time.

Common mistakes

• Forgetting to double the 9 s rise and answering 9 s for the total time.
• Using v = gt for the height instead of v₀² = 2gh.

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