Falling objects - Using the Quadratic Formula

Purpose
Use the quadratic formula to find the time it takes for a ball to drop and hit the ground under the influence of gravity

Part I - Using the Quadratic Formula to find the time for a dropped ball to hit the ground.

Using a strobe light the path of a ball is shown:

The equation of a falling body is given by:

s = (0.5)gt² + v₀t + s₀

where g is gravity, s₀ is the starting height, s is the final height, and v₀ is the starting velocity and t is time.

In metric units the acceleration due to gravity g = 9.8 m/sec².

Each mark on the board is 0.25 meters. Estimate the initial height s₀, of the ball: m

What is the final height s, of the ball (we assume it lands on the ground)? m

What is the initial speed v₀ of the ball? m/s (see video)

Write the equation for the falling ball:

Use the quadratic formula to solve this equation for t and find the time to hit the ground.                     sec

Each strobe flash is 0.06 seconds; estimate from the photo how long the ball took to reach the ground experimentally.                 sec

Part II - Using the Quadratic Formula to find the time for a ball to hit the ground with a given velocity and height.

Use the link below to go to this applet:

Check Show Grid, Show Path, Uncheck Show Velocity; Set the Projection angle to 90^o
To erase the path for another run, uncheck Show Path and then check it. The time to hit the ground shows in the upper right corner.

www.ngsir.netfirms.com/englishhtm/ThrowABall.htm

Use this data for initial velocity and height and your equation

s = (0.5)gt² + v₀t + s₀ with g = 9.8

Initial Velocity and Height
Velocity v_o	Height s_o
20	200
25	150
30	150
40	100
45	100
50	50

Write your equation here:

Algebraic Method:

Find the time to hit the ground (s = 0) using the quadratic formula. sec

Graph your equation and find the vertex either from the graph, or by using the vertex formula. vertex : ( , )

Applet:

Now run the applet using your values for v₀ and s₀ to see the time to hit the ground (upper right).                          sec

Use the grid to determine the highest point of the path.                            m

To find the time at the highest point someone will have to watch the timer to estimate when the path reaches the highest point. time             sec