Let's solve the problem step by step:

Step 1: Identify the given information:
- The particle is thrown upwards from the ground.
- It experiences a constant resistance force that produces a retardation of 2 m/s^2.
- The ratio of the time of ascent to the time of descent is 1:1.
- The acceleration due to gravity is 10 m/s^2 (g=10 m/s^2).

Step 2: Determine the time of ascent and descent:
Since the ratio of the time of ascent to the time of descent is 1:1, we can assume that the time taken for ascent and descent is the same. Let's denote this time as 't'.

Step 3: Calculate the time of ascent and descent:
During the ascent, the particle is moving against the force of gravity and the resistance force. The net acceleration can be calculated as:
Net acceleration = acceleration due to gravity - resistance force
Net acceleration = 10 m/s^2 - 2 m/s^2
Net acceleration = 8 m/s^2

Using the equation of motion:
Final velocity = Initial velocity + (Net acceleration * time)
0 = u - (8 * t) ---(Equation 1)

During the descent, the particle is moving with the force of gravity and the resistance force. The net acceleration can be calculated as:
Net acceleration = acceleration due to gravity + resistance force
Net acceleration = 10 m/s^2 + 2 m/s^2
Net acceleration = 12 m/s^2

Using the equation of motion:
Final velocity = Initial velocity + (Net acceleration * time)
0 = u + (12 * t) ---(Equation 2)

Step 4: Solve the equations:
From Equation 1, we can rearrange it to solve for the initial velocity (u):
u = 8t

Substituting this value of u in Equation 2:
0 = 8t + (12 * t)
0 = 20t

Since time (t) cannot be zero, we can cancel it out from both sides of the equation:
0 = 20

Step 5: Analyze the result:
The equation 0 = 20 is not possible, which means there is no solution for the given problem. It seems there is an error or inconsistency in the given information or problem statement.

Therefore, we cannot determine the ratio of the time of ascent to the time of descent based on the given information.

Question

Let's solve the problem step by step:

Step 1: Identify the given information:
- The particle is thrown upwards from the ground.
- It experiences a constant resistance force that produces a retardation of 2 m/s^2.
- The ratio of the time of ascent to the time of descent is 1:1.
- The acceleration due to gravity is 10 m/s^2 (g=10 m/s^2).

Step 2: Determine the time of ascent and descent:
Since the ratio of the time of ascent to the time of descent is 1:1, we can assume that the time taken for ascent and descent is the same. Let's denote this time as 't'.

Step 3: Calculate the time of ascent and descent:
During the ascent, the particle is moving against the force of gravity and the resistance force. The net acceleration can be calculated as:
Net acceleration = acceleration due to gravity - resistance force
Net acceleration = 10 m/s^2 - 2 m/s^2
Net acceleration = 8 m/s^2

Using the equation of motion:
Final velocity = Initial velocity + (Net acceleration * time)
0 = u - (8 * t)  ---(Equation 1)

During the descent, the particle is moving with the force of gravity and the resistance force. The net acceleration can be calculated as:
Net acceleration = acceleration due to gravity + resistance force
Net acceleration = 10 m/s^2 + 2 m/s^2
Net acceleration = 12 m/s^2

Using the equation of motion:
Final velocity = Initial velocity + (Net acceleration * time)
0 = u + (12 * t)  ---(Equation 2)

Step 4: Solve the equations:
From Equation 1, we can rearrange it to solve for the initial velocity (u):
u = 8t

Substituting this value of u in Equation 2:
0 = 8t + (12 * t)
0 = 20t

Since time (t) cannot be zero, we can cancel it out from both sides of the equation:
0 = 20

Step 5: Analyze the result:
The equation 0 = 20 is not possible, which means there is no solution for the given problem. It seems there is an error or inconsistency in the given information or problem statement.

Therefore, we cannot determine the ratio of the time of ascent to the time of descent based on the given information.

Knowee AI · Accepted Answer