How long does it take for a golf ball to fall from rest for a distance of 11.2 m? How far would the ball fall in twice that time?
Use this equation to answer your questions:
t = sqrt(2H/g)
H increases with the square of time. Doubling t quadruples the distance it falls.
tennis
To calculate the time it takes for a golf ball to fall from rest for a distance of 11.2 m, we can use the formula for gravitational acceleration. The equation for the time of free fall is:
t = √(2h/g)
Where:
t is the time in seconds,
h is the height or distance fallen in meters,
g is the gravitational acceleration, which is approximately 9.8 m/s² on Earth.
Now let's substitute the values into the equation:
t = √(2 * 11.2 / 9.8)
t = √(22.4 / 9.8)
t = √2.2857
t ≈ 1.51 seconds
Therefore, it takes approximately 1.51 seconds for the golf ball to fall from rest for a distance of 11.2 m.
To find how far the ball would fall in twice that time, we can use the equation for distance fallen in free fall:
h = 0.5gt²
Let's find the distance fallen for twice the time:
d = 0.5 * 9.8 * (2 * 1.51)²
d = 0.5 * 9.8 * 4.5581
d ≈ 22.4167 meters
Therefore, the ball would fall approximately 22.4167 meters in twice the time it takes to fall 11.2 meters.