Question

The referee at a football game dropped the coin to the ground from a height of 3 feet. About how many seconds did it take for the coin to hit the ground? Use the formula h = -16t^2 + h₀, where h is the height of the coin in feet, t is the time in seconds, and h₀ represents the initial height.

A. Calculating time for the coin to hit the ground
B. Using the formula for free fall in physics
C. Understanding the referee's action in the football game
D. Determining the impact of height on time

Answer 1

To find the time it takes for a coin to hit the ground when dropped from a height of 3 feet, the formula h = -16t^2 + h₀ is used. After rearranging the equation and solving for t, we find the time t to be approximately 0.433 seconds.

Step-by-step explanation:

To determine how long it took for the coin to hit the ground after being dropped from a height of 3 feet, we use the formula h = -16t^2 + h₀, where h is the height of the coin in feet above the ground, t is the time in seconds, and h₀ is the initial height from which the coin was dropped. In this case, h becomes 0 when the coin hits the ground, and the initial height h₀ is 3 feet. The formula then becomes 0 = -16t^2 + 3. To find the time t, we need to solve this quadratic equation for t.

Let's rearrange the equation to get 16t^2 = 3. Then we take the square root of both sides to get t = √(3/16). After calculating this, we find that t is approximately 0.433 seconds. This is the time it takes for the coin to drop from a height of 3 feet to the ground.