Question

A winding drum raises a cage through a height of 120 m. the cage has, at first, an accelerationof 1.5 m/s^2 until the velocity of 9 m/s is reached, after which the velocity is constant until the cage nears the top, when the final retardation is 6 m/s^2. find the time taken for the cage to reach the top.

Answer 1

Solution

Answer 2

345

Answer 3

Can any one give what be the solution

Answer 4

17.1s

Answer 5

yawa panga bogo ninyo

Answer 6

17.1 sec

Answer 7

[AI-generated answer — Explain Bot]

To solve this problem, we will divide it into three parts:

1. The initial acceleration phase.
2. The constant velocity phase.
3. The final retardation phase.

1. Initial Acceleration Phase:
We are given that the initial acceleration of the cage is 1.5 m/s^2 until it reaches a velocity of 9 m/s.

To find the time taken for the initial acceleration phase, we can use the equation:
v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

Here, the initial velocity u is 0 m/s (as the cage starts from rest), the final velocity v is 9 m/s, and the acceleration a is 1.5 m/s^2.

Using the equation v = u + at, we can rearrange it to solve for t:
t = (v - u) / a

Substituting the values, we get:
t = (9 - 0) / 1.5 = 6 seconds (time for the initial acceleration phase).

2. Constant Velocity Phase:
During this phase, the velocity remains constant at 9 m/s.

To find the time taken for the constant velocity phase, we can use the equation:
distance = velocity × time

The distance traveled during this phase is equal to the height raised, which is 120 m. The velocity remains constant at 9 m/s. Let's calculate the time taken during this phase:

t = distance / velocity = 120 / 9 = 13.33 seconds (approx)

3. Final Retardation Phase:
During this phase, the cage decelerates with a retardation of 6 m/s^2 until it comes to a stop at the top.

Using the equation:
v = u + at

Here, the final velocity v is 0 m/s (as the cage comes to a stop), the initial velocity u is 9 m/s, and the retardation a is -6 m/s^2 (negative sign indicates deceleration).

We can rearrange the equation to solve for t:
t = (v - u) / a

Substituting the values, we get:
t = (0 - 9) / (-6) = 1.5 seconds (time for the final retardation phase).

To find the total time taken for the cage to reach the top, we sum up the times taken for each phase:

Total time = time for initial acceleration + time for constant velocity + time for final retardation
= 6 seconds + 13.33 seconds + 1.5 seconds
= 20.83 seconds (approx)

Therefore, it takes approximately 20.83 seconds for the cage to reach the top.