a bungee jumper is falling at a velocity of 2m/s [down] when the bungee cord just starts to stretch. after the cord stretches for 2.5s, the velocity is 11m [down]. assume that the acceleration is at constant.
a) what is the acceleration of the jumper?
b) what is the total time for the jumper to slow down from 25m/s [down] to zero?
show all ur steps pls
To find the acceleration of the jumper, we can use the formula:
v = u + at
where:
- v is the final velocity (11 m/s)
- u is the initial velocity (2 m/s)
- a is the acceleration (which we want to find)
- t is the time taken (2.5 s)
Using this formula, we can solve for acceleration (a).
11 m/s = 2 m/s + a * 2.5 s
Subtracting 2 m/s from both sides:
9 m/s = a * 2.5 s
Divide both sides by 2.5 s:
a = 9 m/s / 2.5 s
a = 3.6 m/s^2
Therefore, the acceleration of the jumper is 3.6 m/s^2.
Next, to find the total time for the jumper to slow down from 25 m/s [down] to zero, we can use the formula:
v = u + at
where:
- v is the final velocity (0 m/s)
- u is the initial velocity (25 m/s)
- a is the acceleration (-3.6 m/s^2)
- t is the time taken (which we want to find)
Using this formula, we can solve for time (t).
0 m/s = 25 m/s + (-3.6 m/s^2) * t
Subtracting 25 m/s from both sides:
-25 m/s = -3.6 m/s^2 * t
Divide both sides by -3.6 m/s^2:
t = -25 m/s / -3.6 m/s^2
t = 6.94 s
Therefore, the total time for the jumper to slow down from 25 m/s [down] to zero is approximately 6.94 seconds.
To begin, let's assign some variables:
Initial velocity (u) = -2 m/s (negative because it’s downwards)
Final velocity (v) = -11 m/s (negative because it’s downwards)
Time (t) = 2.5 s
To calculate the acceleration of the jumper (a):
a = (v - u) / t
Substituting the given values:
a = (-11 - (-2)) / 2.5
a = (-11 + 2) / 2.5
a = -9 / 2.5
a = -3.6 m/s²
Therefore, the acceleration of the jumper is -3.6 m/s² (negative because it’s downwards).
Now, let's move on to the second part of the question:
Initial velocity (u) = -25 m/s (negative because it’s downwards)
Final velocity (v) = 0 m/s
Acceleration (a) = -3.6 m/s² (negative because it’s downwards)
To find the total time (t) to slow down from 25 m/s to 0 m/s, we can use the equation:
v = u + at
Rearranging the equation, we can find the time:
t = (v - u) / a
Substituting the given values:
t = (0 - (-25)) / -3.6
t = (0 + 25) / -3.6
t = 25 / -3.6
t ≈ -6.94 s
The time obtained (-6.94 s) is negative. This indicates that there may have been an error in the calculations or in the given values. Double-checking the equation and the variables is recommended to ensure accurate results.