i posted this question before however i did not understand drwls explanation. anybody else want to try ?

Sam tosses a ball horizontally off a footbridge at 3.1 m/s. How much time passes after he releases it until its speed doubles?

Well, it is easy if one considers energy.

if velocity doubles, then velocity quadruples

Vf^2=4Vi^2
but also we know from energy,
Vf^2=Vi^2+2*g*h where h is the distance fell.

so
4Vi^2=Vi^2+2gh
h= 3Vi^2/2g
Now how much time passes for it to go h?

average velocity= (Vf+Vi)/2= 3Vi/2
time= h/avg velocity= you do it. You know Vi

does stand for gravity?

g is the acceleration due to gravity, 9.8m/s^2

hmm i somehow got .3161 but that's wrong according to my online instructor.hmm

To solve this problem, you can use the principles of physics and the laws of motion.

First, let's consider the motion of the ball after Sam releases it horizontally from the footbridge. We'll assume there are no external forces acting on the ball apart from gravity.

Since the ball is released horizontally, its initial vertical velocity is zero. However, the ball experiences constant acceleration in the vertical direction due to gravity. The acceleration due to gravity, denoted by 'g', is approximately 9.8 m/s^2.

Now, let's break down the motion of the ball into its horizontal and vertical components.

1. Horizontal Motion:
When the ball is tossed horizontally, its horizontal velocity remains constant throughout. This means that the horizontal acceleration is zero, and the horizontal distance traveled by the ball is given by the equation:
distance = velocity * time

Given that the initial horizontal velocity is 3.1 m/s, the time it takes for the speed to double can be found by using the following equation:
2 * 3.1 m/s = 3.1 m/s * time
(time is the unknown variable we're trying to solve for)

Simplifying this equation, we get:
6.2 m/s = 3.1 m/s * time

To find the value of time, we can divide both sides of the equation by 3.1 m/s:
time = 6.2 m/s / 3.1 m/s
time = 2 seconds

Therefore, the time it takes for the speed of the ball to double is 2 seconds.

2. Vertical Motion:
Although the vertical motion is not directly related to the answer we seek, it's important to understand that the velocity in the vertical direction increases due to gravity. That's why the vertical velocity component changes over time while the horizontal velocity remains constant. The physics behind this motion involves the equations of kinematics and projectile motion. However, for this specific question, we don't need to delve deeper into the vertical motion.

I hope this explanation helps you understand how to solve the problem. If you have any further questions, feel free to ask!