A golf ball is dropped from rest from a height of 8.30 m. It hits the pavement, then bounces back up, rising just 5.00 m before falling back down again. A boy then catches the ball when it is 1.10 m above the pavement. Ignoring air resistance, calculate the total amount of time that the ball is in the air, from drop to catch.
Basic kinetmatics stuff. Use
s = ½at² to find the time to fall s = 8.3m
Then use kinematics to find the time to fall 5.0m
(It's actually rising, but time to fall = time to rise, and fall time is easier to calculate (no initial v)!)
Then use kinematics to find the time to fall (5.0m - 1.1m).
Add the three times for your answer.
btw what school u go to
To calculate the total amount of time the ball is in the air, we can break the problem into two parts: the ball's descent and its ascent.
First, we'll calculate the time it takes for the ball to fall from its initial height of 8.30 m to the pavement. We can use the equation for free fall:
s = 0.5 * g * t^2
Where:
s = distance
g = acceleration due to gravity (9.8 m/s^2)
t = time
Rearranging this equation, we get:
t = sqrt(2s / g)
Substituting the values, we have:
t(descent) = sqrt(2 * 8.30 m / 9.8 m/s^2)
Calculating this, we find that t(descent) ≈ 1.24 seconds.
Next, we'll calculate the time it takes for the ball to rise from the pavement to its maximum height of 5.00 m. Since the ball is bouncing, we know that its velocity just before impact must be the same as its velocity just after leaving the pavement. This means that the time of ascent will be the same as the time of descent.
So, t(ascent) = t(descent) ≈ 1.24 seconds.
Finally, we can calculate the total time the ball is in the air by adding the descent time, the ascent time, and the time it takes to catch it:
Total time = t(descent) + t(ascent) + t(catch)
Given that the ball is caught when it is 1.10 m above the pavement, we can use the equation for free fall again to find the catch time:
t = sqrt(2s / g)
t(catch) = sqrt(2 * 1.10 m / 9.8 m/s^2)
Calculating this, we find that t(catch) ≈ 0.47 seconds.
Now, we can calculate the total time:
Total time = 1.24 seconds + 1.24 seconds + 0.47 seconds
Total time ≈ 2.95 seconds
Therefore, the ball is in the air for approximately 2.95 seconds.