Answer:
31.55 m/s
Explanation:
Let the initial velocity of the arrow is u metre per second.
Angle of projection, θ = 40 degree
range = 100 m
Use the formula for the range.

100 = u^2 Sin(2 x 40) / 9.8
100 x 9.8 = u^2 Sin 80
u^2 = 995.11
u = 31.55 m/s
Answer:
v₀ = 280.6 m / s
Explanation:
we have the shock between the bullet and the block that we can work with at the moment and another part where the assembly (bullet + block) compresses a spring, which we can work with mechanical energy,
We write the mechanical energy when the shock has passed the bodies
Em₀ = K = ½ (m + M) v²
We write the mechanical energy when the spring is in maximum compression

½ (m + M) v² = ½ k x²
Let's calculate the system speed
v = √ [k x² / (m + M)]
v = √[152 ×0.78² / (0.012 +0.109) ]
v = 27.65 m / s
This is the speed of the bullet + Block system
Now let's use the moment to solve the shock
Before the crash
p₀ = m v₀
After the crash

The system is formed by the bullet and block assembly, so the forces during the crash are internal and the moment is preserved

m v₀ = (m + M) v
v₀ = v (m + M) / m
let's calculate
v₀ = 27.83 (0.012 +0.109) /0.012
v₀ = 280.6 m / s
Answer:
Explanation:
From the given information:
We know that the thin spherical shell is on a uniform surface which implies that both the inside and outside the charge of the sphere are equal, Then
The volume charge distribution relates to the radial direction at r = R
∴



To find the constant k, we examine the total charge Q which is:


∴



Thus;




Hence, from equation (1), if k = 


To verify the units:

↓ ↓ ↓
c/m³ c/m³ × 1/m
Thus, the units are verified.
The integrated charge Q



since 
