A popular entertainment at some carnivals is the blanket toss.
(a) If a person is thrown to a maximum height of 26.0 ft above the blanket, how long does she spend in the air?
(b) Is the amount of time the person is below a height of 13.0 ft more than, less than, or equal to the amount of time the person is above a height of 13.0 ft?
Explain
(c) Verify your answer to part (b) with some calculations.
_______ s (time below 13.0 ft)
_______ s (time above 13.0 ft)
(a) Twice the fall time (t) from a height of h = 26 ft.
The fall time t is given by
(g/2)t^2 = h
So,
t = sqrt(2h/g)= 1.27 s
Use g = 32.2 ft/s^2
2t = 2.54 s
(b) Average speed is lower at the top half. That makes the time spent there longer than is is on the bottom half.
(c) Calculate the time it takes to fall 13.0 ft starting at velocity 0 . I get 0.899 s
1.27 s minus that time is the time spent in the lower half
a. t=sqrt(2h/g)=1.27s(2)= 2.54 s
b. the amount of time the person is above the height of 13.0 ft is more than the amount of time that person is below the height of 13.0 ft
c. x=vt+1/2at^2=0.933 s
1.27 s-0.933 s=0.371 s in the lower half
can you show how part C is calculate?
Don't forget to multiply your answer for C by 2, to get the total time!
^^^ you're a life saver
(a) To find the time spent in the air, we can use the kinematic equation:
h = ut + (1/2)gt^2
where h is the maximum height (26.0 ft), u is the initial vertical velocity (0 ft/s as they start from rest), g is the acceleration due to gravity (32.2 ft/s^2), and t is the time in seconds.
Rearranging the equation to solve for time (t), we have:
t = √((2h) / g)
Plugging in the values, we get:
t = √((2 * 26.0 ft) / 32.2 ft/s^2)
t ≈ √(52.0 ft / 32.2 ft/s^2)
t ≈ √1.615 ≈ 1.27 s
Therefore, the person spends approximately 1.27 seconds in the air.
(b) To determine whether the time below a height of 13.0 ft is more, less, or equal to the time above a height of 13.0 ft, we need to analyze the motion of the person during the toss.
Since the person is thrown upwards and reaches a maximum height before coming back down, the time spent above a height of 13.0 ft will be equal to the time spent below 13.0 ft. This is because the motion is symmetric, meaning the time it takes to reach the maximum height is equal to the time it takes to descend back down to the same reference point.
Therefore, the time below 13.0 ft is equal to the time above 13.0 ft.
(c) To verify our answer in part (b), we can calculate the time spent below and above 13.0 ft.
When the person is falling back below 13.0 ft, it will take the same amount of time as it did to reach the maximum height. So, the time below 13.0 ft is also 1.27 seconds.
Similarly, the time above 13.0 ft is also 1.27 seconds, as it takes the same amount of time to descend from the maximum height to 13.0 ft as it took to ascend from 13.0 ft to the maximum height.
Therefore,
Time below 13.0 ft = 1.27 seconds
Time above 13.0 ft = 1.27 seconds