Let the cup is filled to height h after some time
now the total volume of coffee filled in the cup is given as
now volume of the coffee will be
here we know that
now we know that volume flow rate is given as
here y = 3 cm
so water will rise up with speed 0.71 cm/s
Conservation of energy means that initial kinetic energy =maximum gravitational potential energy. 1/2 * 3 * 10^2 = 150J. The gravitational potential energy at the top is 150 joules. The gravitational potential energy is calculated through mgh, so 150 = 3 * 10 * h. Height is 5 meters
Answer:
The plane will be 11545.46 m far when the observer hears the sonic boom
Explanation:
Step 1: Data given
Altitude of the plane = 7800 meters
speed of sound = 311.83 m/s
Step 2:
The mach number M = vs/v
This means v/vs = 1/M
Half- angle = ∅
sin∅= v/vs
∅ = sin^-1 (v/vs)
∅ = sin^-1 (1/M)
∅ = sin^-1(1/1.48)
∅= 42.5 °
tan ∅ = h/x
⇒ with h= the altitude of the plane = 7800 meter
⇒ with x = the horizontal distance moved by the plane
x = h/tan ∅
x = 7800 / tan 42.5
x = 8512.2 meters
d = the distance between the observer and the plane when the observer hears the sonic boom is:
d = √(8512.2² + 7800²)
d = 11545.46 m
The plane will be 11545.46 m far when the observer hears the sonic boom