Answer: North of west
Explanation:
Given
Plane wishes to fly in west
but wind with speed 33.9 km/h towards south obstructing its path
so plane must fly at an angle of \theta w.r.t west such that it final velocity is towards west
Plane absolute speed=195 km/h
To fly towards west velocity in Y direction should be zero
thus
so Plane should head towards North of west in order to fly in west.
So plane
actual velocity is
solution:
As Given plane is flying in east direction.
It throws back some supplies to designated target.
Time taken by the supply to reach the target =10 seconds
g = Acceleration due to gravity = - 9.8 m/s²[Taken negative as object is falling Downwards]
As we have to find distance from the ground to plane which is given by d.
d =
= meters
Distance from the ground where supplies has to be land to plane = Option B =490 meters
Answer:
a) h=3.16 m, b) v_{cm }^ = 6.43 m / s
Explanation:
a) For this exercise we can use the conservation of mechanical energy
Starting point. Highest on the hill
Em₀ = U = mg h
final point. Lowest point
= K
Scientific energy has two parts, one of translation of center of mass (center of the sphere) and one of stationery, the sphere
K = ½ m + ½
w²
angular and linear speed are related
v = w r
w = v / r
K = ½ m v_{cm }^{2} + ½ I_{cm} v_{cm }^{2} / r²
Em_{f} = ½ v_{cm }^{2} (m + I_{cm} / r2)
as there are no friction losses, mechanical energy is conserved
Em₀ = Em_{f}
mg h = ½ v_{cm }^{2} (m + I_{cm} / r²) (1)
h = ½ v_{cm }^{2} / g (1 + I_{cm} / mr²)
for the moment of inertia of a basketball we can approximate it to a spherical shell
I_{cm} = ⅔ m r²
we substitute
h = ½ v_{cm }^{2} / g (1 + ⅔ mr² / mr²)
h = ½ v_{cm }^{2}/g 5/3
h = 5/6 v_{cm }^{2} / g
let's calculate
h = 5/6 6.1 2 / 9.8
h = 3.16 m
b) this part of the exercise we solve the speed of equation 1
v_{cm }^{2} = 2m gh / (1 + I_{cm} / r²)
in this case the object is a frozen juice container, which we can simulate a solid cylinder with moment of inertia
I_{cm} = ½ m r²
we substitute
v_{cm } = √ [2gh / (1 + ½)]
v_{cm } = √(4/3 gh)
let's calculate
v_{cm } = √ (4/3 9.8 3.16)
v_{cm }^ = 6.43 m / s