Answer:
m = 3.91 kg
Explanation:
Given that,
Mass of the object, m = 3.74 kg
Stretching in the spring, x = 0.0161 m
The frequency of vibration, f = 3.84 Hz
When the object is suspended, the gravitational force is balanced by the spring force as :



k = 2276.52 N/m
The frequency of vibration is given by :



m = 3.91 kg
So, the mass of the object is 3.91 kg. Hence, this is the required solution.
Explanation :
The forces acting on hot- air balloon are:
Weight, (W)
Force due to air resistance, (F)
Upthrust force, (U)
Its weight W is acting in downward direction. The upthrust force U acts in upward direction. When the balloon is moving upward, the air resistance is in downward and vice versa.
In this case, the hot-air balloon descends vertically at constant speed.
so, 
and 
so,
....................(1)
when it is ascending let the weight that it is releasing is R, so
..........(2)
solving equation (1) and (2)

2F is the weight of material that must be released from the balloon so that it ascends vertically at the same constant speed.
Answer:
The time taken by the projectile to hit the ground is 6.85 sec.
Explanation:
Given that,
Vertical height of cliff = 230 m
Distance = 300 m
Suppose, determine the time taken by the projectile to hit the ground.
We need to calculate the time
Using second equation of motion

Where, s = vertical height of cliff
u = initial vertical velocity
g = acceleration due to gravity
Put the value in the equation



Hence, The time taken by the projectile to hit the ground is 6.85 sec.