---
title: "A small ball is dropped from rest from a height \\(H\\) above the ground and takes a time \\(T\\) to reach the ground. In a second trial, the ball is thrown vertically upward from the same height \\(H\\) with an initial speed such that the ball reaches a maximum height of \\(2H\\) above the ground before falling back down. Air resistance is negligible.   What is the total time the ball is in the air during the second trial in terms of \\(T\\)?"
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url: "https://nerd-notes.com/ubq/114030/"
date_modified: "2026-06-22T09:46:03+00:00"
---

# A small ball is dropped from rest from a height \(H\) above the ground and takes a time \(T\) to reach the ground. In a second trial, the ball is thrown vertically upward from the same height \(H\) with an initial speed such that the ball reaches a maximum height of \(2H\) above the ground before falling back down. Air resistance is negligible. 

What is the total time the ball is in the air during the second trial in terms of \(T\)?

A small ball is dropped from rest from a height \(H\) above the ground and takes a time \(T\) to reach the ground. In a second trial, the ball is thrown vertically upward from the same height \(H\) with an initial speed such that the ball reaches a maximum height of \(2H\) above the ground before falling back down. Air resistance is negligible. 

What is the total time the ball is in the air during the second trial in terms of \(T\)?

![Two side-by-side diagrams of a ball's motion. The left diagram, labeled Trial 1, shows a ball at height H being dropped straight down to the ground. The right diagram, labeled Trial 2, shows a ball at the same starting height H being thrown upward, reaching a peak at height 2H, and then falling straight down to the ground. The ground is indicated by a horizontal line at height zero. Vertical dashed lines with arrows indicate the heights H and 2H.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/kinematics-setup-1782121562-o1FKLW.jpg)

- **A.** \(\sqrt{2}T\)
- **B.** \(2T\)
- **C.** \((1 + \sqrt{2})T\)
- **D.** \(3T\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/114030/*