a)
Y₀ = initial position of the stone at the time of launch = 0 m
Y = final position of stone = 20.0 meters
a = acceleration = - 9.8 m/s²
v₀ = initial speed of stone at the time of launch = 30.0 m/s
v = final speed = ?
Using the equation
v² = v₀² + 2 a (Y - Y₀)
inserting the values
v² = 30² + 2 (- 9.8) (20 - 0)
v = 22.5 m/s
b)
Y₀ = initial position of the stone at the time of launch = 0 m
Y = maximum height gained
a = acceleration = - 9.8 m/s²
v₀ = initial speed of stone at the time of launch = 30.0 m/s
v = final speed = 0 m/s
Using the equation
v² = v₀² + 2 a (Y - Y₀)
inserting the values
0² = 30² + 2 (- 9.8) (Y - 0)
Y = 46 m
Answer:
The time constant is 
Explanation:
From the question we are told that
The spring constant is 
The mass of the ball is 
The amplitude of the oscillation t the beginning is 
The amplitude after time t is 
The number of oscillation is 
Generally the time taken to attain the second amplitude is mathematically represented as
Here T is the period of oscillation
=> 
=> 
Generally the amplitude at time t is mathematically represented as
Here a is the damping constant so
at ,
So
=> 
taking natural log of both sides
=> 
=> 
Generally the time constant is mathematically represented as
=> 
=>
Answer:
Δ h = 52.78 m
Explanation:
given,
Atmospheric pressure at the top of building = 97.6 kPa
Atmospheric pressure at the bottom of building = 98.2 kPa
Density of air = 1.16 kg/m³
acceleration due to gravity, g = 9.8 m/s²
height of the building = ?
We know,
Δ P = ρ g Δ h
(98.2-97.6) x 10³ = 1.16 x 9.8 x Δ h
11.368 Δ h = 600
Δ h = 52.78 m
Hence, the height of the building is equal to 52.78 m.
