Question

During a halftime show, a baton twirler releases her baton from a point 4 feet above the ground with an initial vertical velocity of 25 feet per second. How long will it take for the baton to reach the ground?

Option 1: 1 second
Option 2: 2 seconds
Option 3: 3 seconds
Option 4: 4 seconds

Answer 1

To find out how long it will take for the baton to reach the ground, we can use the equation of motion for vertical free fall. The time it takes for the baton to reach the ground is approximately 0.87 seconds.

Therefore, Option 1: 1 second is closest to the correct answer.

Step-by-step explanation:

To find out how long it will take for the baton to reach the ground, we can use the equation of motion for vertical free fall:

h = ut + (1/2)gt^2

Where h is the initial height, u is the initial velocity, g is the acceleration due to gravity, and t is the time. In this case, h = 4 feet, u = 25 feet per second, and g = 32 feet per second squared.

Substituting these values into the equation, we get:

4 = 25t + (1/2)(32)t^2

After rearranging the equation and simplifying it, we get a quadratic equation:

(1/2)(32)t^2 + 25t - 4 = 0

Solving this quadratic equation, we find that the time it takes for the baton to reach the ground is approximately 0.87 seconds. Therefore, Option 1: 1 second is closest to the correct answer.