Answer:
3.53 m/s
Explanation:
KE₁ + RE₁ = KE₂ + RE₂ + PE
½ mv₁² + ½ Iω₁² = ½ mv₂² + ½ Iω₂² + mgh
For a solid sphere, I = ⅖ mr²
½ mv₁² + ½ (⅖ mr²) ω₁² = ½ mv₂² + ½ (⅖ mr²) ω₂² + mgh
½ mv₁² + ⅕ mr² ω₁² = ½ mv₂² + ⅕ mr² ω₂² + mgh
Rolling without slipping means v = ωr.
½ mv₁² + ⅕ mv₁² = ½ mv₂² + ⅕ mv₂² + mgh
⁷/₁₀ mv₁² = ⁷/₁₀ mv₂² + mgh
⁷/₁₀ v₁² = ⁷/₁₀ v₂² + gh
Substitute:
⁷/₁₀ (5.50 m/s)² = ⁷/₁₀ v₂² + (9.8 m/s²) (3.00 m sin 25.0°)
v₂ = 3.53 m/s
1. The time for a radioactive sample to reduce to half of its original mass.
4. 10% of 232 is 23.2 times 6 equals 139.2
68.9 x6 equals 413.4
5. 0.37kg
6. 2000 years
7. 6.84 seconds
Answer : The total work done in raising the ball is, 0.98 J
Explanation : Given,
Mass of the ball = 0.075 kg
Height raised of the ball = 1.33 m
As we know that the object is moving with the constant velocity, that means the work done against the gravity will be the net-work done.
So, the work done will be:

where,
w = work done
m = mass of ball
h = height of ball
g = acceleration due of gravity = 
Now put all the given values in the above formula, we get:


Thus, the total work done in raising the ball is, 0.98 J
The answer is A. Cones, as rods are not sensitive to color. :)
Answer:
The phase difference between these two waves is 141.1⁰
Explanation:
The displacement of the wave is given as;

Amplitude, A = 2yₓCos(¹/₂Φ)
Since the amplitude of the combination is 1.5 times that of one of the original amplitudes = yₓ = 1.5 × A = 1.5A
A = 2(1.5A)Cos(¹/₂Φ)
A = 3ACos(¹/₂Φ)
¹/₃ = Cos(¹/₂Φ)
(¹/₂Φ) = Cos ⁻(0.3333)
(¹/₂Φ) = 70.55°
Φ = 141.1°
The phase difference between these two waves is 141.1⁰