Question

If I drop a ball off of a civic center (approximately 100.0 tall), how many seconds later does it hit the ground?

A) 1 second
B) 2 seconds
C) 3 seconds
D) 4 seconds

Answer 1

To calculate the time it takes for a ball to hit the ground when dropped from a 100.0-meter height, we use the free fall formula and solve for time, yielding approximately 4.52 seconds. Therefore, the closest full second is 4 seconds (Option D).

Step-by-step explanation:

To determine how many seconds later the ball hits the ground when dropped from a 100.0-meter-tall civic center, we use the formula for free fall: distance (d) = ½ * gravity (g) * time (t)^2. Assuming the acceleration due to gravity is 9.8 m/s2, and ignoring air resistance, we can set up the equation as follows:

d = ½ * g * t2

100.0 = ½ * 9.8 * t2

This simplifies to:

100.0 = 4.9 * t2

Now we solve for t2:

t2 = 100.0 / 4.9 ≈ 20.41

And then take the square root to solve for t:

t = √20.41 ≈ 4.52 seconds

However, since we need to select the closest full second for the answer options provided, the correct choice is (D) 4 seconds. The ball will hit the ground approximately 4 seconds after being dropped.