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
Answer:
Assuming the given radius is 10⁶ km, the radius of the second planet is 1.31 * 10⁶ km.
Explanation:
Newton's law of gravity:
(1)
Centripetal force:
(2)
On a circular orbit both forces must be equal:
(3)
Solving for ω:
(4)
The period T is given by:
(5)
Taking the ratio of two periods:
(6)
Solving for r₁:
(7)
Explanation:
It is given that,
The total mass of the wagon, rider and the rock is 99 kg
The mass of the rock is 0.261 kg.
The initial speed of the wagon, u = 0.519 m/s
Speed of the rock, u' = 15.9 m/s
(a) Let v is the speed of the wagon after the rock is thrown directly in forward direction.
The momentum will remain constant. Using the conservation of momentum as :
v = 0.22 m/s
(b) Let v' is the speed of the wagon after the rock is thrown directly in opposite direction, u' = -15.9 m/s
v' = 0.304 m/s
Hence, this is the required solution.
Answer:
The formula for kinetic energy is K = 1 2 m v 2 K = \dfrac{1}{2}mv^2 K=21mv2