Ball thrown straight up: height and total ti

A ball is thrown straight up at 20 m/s (g = 10). Find the maximum height and the total time until it returns.

Step-by-step

1. h = v₀²/(2g) = 20²/(2×10) = 20
   The upward leg ends at speed 0, and v₀² = 2gh gives the maximum height
2. t = 2v₀/g = 2×20/10 = 4
   Rising and falling take equal times, so the total is 2 times the rise time

Why it works

At the highest point the speed is zero, so v₀² = 2gh gives the height. Going up and coming down take equal time, so the total time is twice the rise time.

Common mistakes

• Forgetting to double the rise time.
• Using g = 9.8 when the question specifies 10.

Related

projectile-motion meeting-problem n-phy-vertical-throw-1