A bungee jumper falls for 1.3 seconds before the bungee cord begins to stretch. Until the jumper has bounced back up to this level, the bungee causes the jumper to have an acceleration upward of 4 m/s2.
a. How fast is the jumper going when the bungee cord begins to stretch? (HINT: this is free fall.)
b. How far below the diving platform is the jumper at that moment?
c. How long after the bungee cord begins to stretch does the jumper reach the
low point of the drop? HINT: The acceleration is different now, in both size
and direction.
d. How far below the diving platform is the jumper at the instant that the speed is zero?
a. To find the speed at which the jumper is going when the bungee cord begins to stretch, we can use the equation of motion for free fall:
v = u + at
Where:
v = final velocity (unknown)
u = initial velocity (0 m/s, as the jumper is at rest before falling)
a = acceleration due to gravity (-9.8 m/s^2)
Since the jumper falls for 1.3 seconds before the bungee cord starts stretching, we can substitute these values into the equation:
v = 0 + (-9.8) * 1.3
v = -12.74 m/s
Therefore, the jumper is traveling at a speed of approximately 12.74 m/s in the downward direction when the bungee cord begins to stretch.
b. To find how far below the diving platform the jumper is at that moment, we can use another equation of motion for free fall:
s = ut + (1/2)at^2
Where:
s = displacement (unknown)
u = initial velocity (0 m/s)
t = time (1.3 seconds)
a = acceleration due to gravity (-9.8 m/s^2)
Substituting the values into the equation:
s = 0 * 1.3 + (1/2) * (-9.8) * (1.3)^2
s = -8.849 m
Therefore, the jumper is approximately 8.849 meters below the diving platform when the bungee cord begins to stretch.
c. After the bungee cord begins to stretch, the jumper experiences an upward acceleration of 4 m/s^2. To find how long it takes for the jumper to reach the low point of the drop, we can use the equation of motion:
v = u + at
Where:
v = final velocity (0 m/s, as the jumper momentarily comes to a stop at the low point)
u = initial velocity (-12.74 m/s, as the jumper was traveling downward at this speed)
a = acceleration (4 m/s^2, in the upward direction)
Substituting the values into the equation:
0 = -12.74 + 4t
4t = 12.74
t = 3.185 seconds
Therefore, it takes approximately 3.185 seconds for the jumper to reach the low point of the drop after the bungee cord begins to stretch.
d. To find how far below the diving platform the jumper is at the instant that the speed is zero, we can again use the equation of motion:
s = ut + (1/2)at^2
Where:
s = displacement (unknown)
u = initial velocity (-12.74 m/s, as the jumper was traveling downward at this speed)
t = time (unknown)
a = acceleration (4 m/s^2, in the upward direction)
To find the time (t) when the speed is zero, we use the fact that the final velocity (v) is zero:
v = u + at
0 = -12.74 + 4t
From here, we can solve for t:
4t = 12.74
t = 3.185 seconds
Substituting the value of t back into the equation:
s = -12.74 * 3.185 + (1/2) * 4 * (3.185)^2
s ≈ -20.244 meters
Therefore, the jumper is approximately 20.244 meters below the diving platform at the instant when the speed is zero.