Abungee jumper falls for 1.3 s before the bungee cord begins tostretch. Until the jumper has bounced back up to this level, thebungee causes the jumpe

A) To find the speed of the jumper when the bungee cord begins to stretch, we can use the formula for average acceleration:
$\text{Average acceleration}=\frac{\text{Change in velocity}}{\text{Time taken}}$
In this case, the average acceleration is given as $4{\text{m/s}}^2$. The time taken for the bungee cord to begin stretching is given as $1.3\text{s}$. We need to find the change in velocity.
Since the average acceleration is constant, we can use the formula:
$\text{Change in velocity}=\text{Average acceleration}\times \text{Time taken}$
Substituting the given values:
$\text{Change in velocity}=4{\text{m/s}}^2\times 1.3\text{s}$
Therefore, the speed of the jumper when the bungee cord begins to stretch is $5.2\text{m/s}$.
B) To find how far below the diving platform the jumper is at that moment, we can use the formula for displacement:
$\text{Displacement}=\text{Initial velocity}\times \text{Time taken}+\frac{1}{2}\times \text{Average acceleration}\times {\text{Time taken}}^2$
At the moment the bungee cord begins to stretch, the initial velocity is zero because the jumper is at the highest point of the fall. The average acceleration is given as $4{\text{m/s}}^2$, and the time taken is $1.3\text{s}$.
Substituting the given values:
$\text{Displacement}=0\times 1.3\text{s}+\frac{1}{2}\times 4{\text{m/s}}^2\times (1.3\text{s}{)}^2$
Therefore, the jumper is $3.38\text{m}$ below the diving platform at that moment.
C) To find the time it takes for the jumper to reach the low point of the drop after the bungee cord begins to stretch, we can consider the symmetry of the motion. The time taken to reach the low point is equal to the time taken to reach the highest point, which is $1.3\text{s}$.
Therefore, the jumper reaches the low point of the drop $1.3\text{s}$ after the bungee cord begins to stretch.
D) To find how far below the diving platform the jumper is at the instant the speed is zero, we can again consider the symmetry of the motion. The displacement at the instant the speed is zero is equal to the displacement at the highest point, which we found in part B to be $3.38\text{m}$.
Therefore, the jumper is $3.38\text{m}$ below the diving platform at the instant the speed is zero.

A) The average acceleration formula can be used to determine the jumper's speed when the bungee cord starts to stretch:
$\text{Average acceleration}=\frac{\text{Change in velocity}}{\text{Time}}$
Since the jumper falls for 1.3 s before the bungee cord begins to stretch, the time can be taken as 1.3 s. The average acceleration is given as 4 m/s². We can rearrange the formula to solve for the change in velocity:
$\text{Change in velocity}=\text{Average acceleration}\times \text{Time}$
Substituting the values:
$\text{Change in velocity}=4{\text{m/s}}^2\times 1.3\text{s}$
Thus, the change in velocity is $4{\text{m/s}}^2\times 1.3\text{s}=5.2\text{m/s}$.
Therefore, the speed of the jumper when the bungee cord begins to stretch is 5.2 m/s.
B) To determine how far below the diving platform the jumper is at that moment, we can use the equation of motion for linear motion:
${\text{Final velocity}}^2={\text{Initial velocity}}^2+2\times \text{Acceleration}\times \text{Distance}$
At the moment the bungee cord begins to stretch, the final velocity is 0 m/s (as the jumper momentarily stops before rebounding), the initial velocity is the speed of the jumper when the bungee cord begins to stretch (5.2 m/s), the acceleration is the average acceleration (4 m/s²), and we want to find the distance.
Rearranging the equation, we have:
$\text{Distance}=\frac{{\text{Final velocity}}^2-{\text{Initial velocity}}^2}{2\times \text{Acceleration}}$
Substituting the values:
$\text{Distance}=\frac{0^2-{5.2}^2}{2\times 4}$
Thus, the distance below the diving platform is $\frac{0^2-{5.2}^2}{2\times 4}=-6.76$ m.
Note that the negative sign indicates that the jumper is below the diving platform.
Therefore, the jumper is 6.76 m below the diving platform at that moment.
C) To determine how long it takes for the jumper to reach the low point of the drop after the bungee cord begins to stretch, we can use the equation of motion:
$\text{Final velocity}=\text{Initial velocity}+\text{Acceleration}\times \text{Time}$
At the low point of the drop, the final velocity is 0 m/s (as the jumper momentarily stops before rebounding), the initial velocity is the speed of the jumper when the bungee cord begins to stretch (5.2 m/s), the acceleration is the acceleration due to gravity (which is approximately -9.8 m/s² since it acts in the opposite direction of the upward motion), and we want to find the time.
Rearranging the equation, we have:
$\text{Time}=\frac{\text{Final velocity}-\text{Initial velocity}}{\text{Acceleration}}$
Substituting the values:
$\text{Time}=\frac{0-5.2}{-9.8}$
Thus, the time it takes for the jumper to reach the low point of the drop after the bungee cord begins to stretch is $\frac{0-5.2}{-9.8}=0.5316$ s.
Therefore, it takes approximately 0.5316 s for the jumper to reach the low point of the drop after the bungee cord begins to stretch.
D) To determine how far below the diving platform the jumper is at the instant the speed is zero, we can again use the equation of motion:
${\text{Final velocity}}^2={\text{Initial velocity}}^2+2\times \text{Acceleration}\times \text{Distance}$
At the instant the speed is zero, the final velocity is 0 m/s, the initial velocity is the speed of the jumper when the bungee cord begins to stretch (5.2 m/s), the acceleration is the acceleration due to gravity (-9.8 m/s²), and we want to find the distance.
Rearranging the equation, we have:
$\text{Distance}=\frac{{\text{Final velocity}}^2-{\text{Initial velocity}}^2}{2\times \text{Acceleration}}$
Substituting the values:
$\text{Distance}=\frac{0^2-{5.2}^2}{2\times -9.8}$
Thus, the distance below the diving platform is $\frac{0^2-{5.2}^2}{2\times -9.8}=-1.3567$ m.
Therefore, the jumper is approximately 1.3567 m below the diving platform at the instant the speed is zero.