Answer:
The answer is below
Explanation:
Charlee's law states that the volume of a gas is directly proportion to the temperature of the gas at constant pressure. That is:
V = kT, where V = volume and T = temperature, k = constant. Therefore:
V / T = k
Given that: 
The new volume is 3.41 m³. That is it expands by 0.41 m³
Answer:
H = 1/2 g t^2 where t is time to fall a height H
H = 1/8 g T^2 where T is total time in air (2 t = T)
R = V T cos θ horizontal range
3/4 g T^2 = V T cos θ 6 H = R given in problem
cos θ = 3 g T / (4 V) (I)
Now t = V sin θ / g time for projectile to fall from max height
T = 2 V sin θ / g
T / V = 2 sin θ / g
cos θ = 3 g / 4 (T / V) from (I)
cos θ = 3 g / 4 * 2 sin V / g = 6 / 4 sin θ
tan θ = 2/3
θ = 33.7 deg
As a check- let V = 100 m/s
Vx = 100 cos 33.7 = 83,2
Vy = 100 sin 33,7 = 55.5
T = 2 * 55.5 / 9.8 = 11.3 sec
H = 1/2 * 9.8 * (11.3 / 2)^2 = 156
R = 83.2 * 11.3 = 932
R / H = 932 / 156 = 5.97 6 within rounding
Answer:
-20.0 m/s and 30.0 m/s
Explanation:
Momentum is conserved:
m (30.0) + m (-20.0) = m v₁ + m v₂
30.0 − 20.0 = v₁ + v₂
10.0 = v₁ + v₂
Since the collision is perfectly elastic, energy is also conserved. Since there's no rotational energy or work done by friction, the initial kinetic energy equals the final kinetic energy.
½ m (30.0)² + ½ m (-20.0)² = ½ mv₁² + ½ mv₂²
(30.0)² + (-20.0)² = v₁² + v₂²
1300 = v₁² + v₂²
We now have two equations and two variables. Solve the system of equations using substitution:
1300 = v₁² + (10 − v₁)²
1300 = v₁² + 100 − 20v₁ + v₁²
0 = 2v₁² − 20v₁ − 1200
0 = v₁² − 10v₁ − 600
0 = (v₁ + 20) (v₁ − 30)
v₁ = -20, 30
If v₁ = -20, v₂ = 30.
If v₁ = 30, v₂ = -20.
So either way, the final velocities are -20.0 m/s and 30.0 m/s.
Answer:
The resultant vector has a magnitude of 4998 m and a direction of 45.7°.
Explanation:
The x component of the resultant vector is the sum of the x components of each individual vector.
x = 3250 cos 38.4 + 1822 cos 58.8
x = 3490.8
Similarly, the y component of the resultant vector is the sum of the y components of each individual vector.
y = 3250 sin 38.4 + 1822 sin 58.8
y = 3577.2
The magnitude can be found with Pythagorean theorem:
√(x² + y²)
√(3490.8² + 3577.2²)
4998
The direction can be found with trigonometry:
atan(y / x)
atan(3577.2 / 3490.8)
45.7°
The resultant vector has a magnitude of 4998 m and a direction of 45.7°.
