Thrown up at 70 m/s: height and time

A ball is thrown straight up at 70 m/s (g = 10 m/s²). Find the maximum height it reaches and the total time until it comes back to where it was thrown.

Step-by-step

1. h = v₀²/(2g) = 70²/(2×10) = 245
   The upward leg ends at speed 0, and v₀² = 2gh gives the maximum height
2. t = 2v₀/g = 2×70/10 = 14
   Rising and falling take equal times, so the total is 2 times the rise time

Why it works

The ball loses 10 m/s of speed every second on the way up and is at rest at the highest point; then it falls back freely, and the fall takes exactly as long as the rise.

Common mistakes

• Dividing 70 m/s by g and calling the result the maximum height.
• Taking only the 7 s rise as the total time.

Related

vertical-throw projectile-motion vertical-throw-60ms-total-time