A golf ball is dropped from rest from a height of 9.60 m. It hits the pavement, then bounces back up, rising just 5.30 m before falling back down again. A boy then catches the ball when it is 1.11 m above the pavement. Ignoring air resistance, calculate the total amount of time that the ball is in the air, from drop to catch.
to drop 9.6m takes √(9.6/4.9)=1.40 seconds
to rise 5.3m takes √(5.3/4.9)=1.04 seconds
to fall 4.19m takes √(4.19/4.9)=0.92 seconds
so, the ball is in the air 3.36 seconds
This is wrong, u cant use t=sqrt of (2d/g) because that is only for when Vo is 0 m/s, when the ball hits the ground the velocity is not 0m/s, therefore when it comes back up the Vo is not 0m/s, the true answer is about 2.32s
To calculate the total amount of time that the ball is in the air, we can use the equations of motion.
We'll break down the motion of the ball into three phases:
1) The ball falling from rest from a height of 9.60 m to the pavement.
2) The ball bouncing back up from the pavement to a height of 5.30 m.
3) The ball falling back down from a height of 5.30 m to be caught at a height of 1.11 m.
Let's calculate the time for each phase:
1) The ball falling from rest from a height of 9.60 m:
Using the equation of motion: h = (1/2) * g * t^2, where h is the height, g is the acceleration due to gravity (9.8 m/s^2), and t is the time.
We can rearrange the equation to solve for time (t): t = sqrt(2h/g).
Substituting the values: t1 = sqrt(2 * 9.60 m / 9.8 m/s^2) = 1.38 s
2) The ball bouncing back up from the pavement to a height of 5.30 m:
The time of flight during the bounce will be equal to the time it took to fall initially, so t2 = t1 = 1.38 s.
3) The ball falling back down from a height of 5.30 m to be caught at a height of 1.11 m:
We'll use the same equation as in phase 1, but with a different height.
t3 = sqrt(2 * (5.30 m - 1.11 m) / 9.8 m/s^2) = sqrt(2 * 4.19 m / 9.8 m/s^2) = 0.92 s
Now we can calculate the total time by summing the times for each phase:
Total time = t1 + t2 + t3 = 1.38 s + 1.38 s + 0.92 s = 3.68 s
Therefore, the total amount of time that the ball is in the air, from drop to catch, is 3.68 seconds.