How Long Does a Horizontally Shot Ball Stay Airborne?

[IneedHelp:-)]

Homework Statement

A ball is shot horizontally at a speed of 10 m/s from a height of 2 meters. How long is the ball in the air and how far horizontally does it travel before it hits the ground.

Homework Equations

V2 Equation

The Attempt at a Solution

I am assuming I need to find both the X and Y components right? I know that the final Y velocity must be 0 because it stops at the top of its trajectory. What is throwing me off is the 2 meters it starts at as well as how I am going to get the horizontal distance.

 

[rock.freak667]

Homework Equations

V2 Equation

[tex]s=s_o +ut-\frac{1}{2}gt^2[/tex]


where s=displacement and s₀= initial displacement.

So considering vertically, what is s₀? and you want to find the 't' for which s=0.

 

[tomcue]

I would approach this problem using the principles of projectile motion. First, I would break the initial velocity of the ball into its x and y components. Since the ball is shot horizontally, the initial velocity in the x-direction is 10 m/s and the initial velocity in the y-direction is 0 m/s.

Next, I would use the equation for the time of flight of a projectile in the y-direction: t = 2vy/g, where t is time, vy is the initial velocity in the y-direction, and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we get t = 2(0)/9.8 = 0 seconds. This means that the ball is in the air for 0 seconds before it hits the ground.

To find the horizontal distance traveled by the ball, I would use the equation x = vxt, where x is the horizontal distance, vx is the initial velocity in the x-direction, and t is the time of flight. Plugging in the values, we get x = (10 m/s)(0 seconds) = 0 meters. This means that the ball travels 0 meters horizontally before hitting the ground.

In conclusion, the ball is in the air for 0 seconds and travels 0 meters horizontally before hitting the ground. This is because the initial velocity in the y-direction is 0, meaning the ball does not have any vertical motion and falls straight down.