Answer:
c. find the slope of the velocity time graph
The addition of vectors involve both magnitude and direction. In this case, we make use of a triangle to visualize the problem. The length of two sides were given while the measure of the angle between the two sides can be derived. We then assign variables for each of the given quantities.
Let:
b = length of one side = 8 m
c = length of one side = 6 m
A = angle between b and c = 90°-25° = 75°
We then use the cosine law to find the length of the unknown side. The cosine law results to the formula: a^2 = b^2 + c^2 -2*b*c*cos(A). Substituting the values, we then have: a = sqrt[(8)^2 + (6)^2 -2(8)(6)cos(75°)]. Finally, we have a = 8.6691 m.
Next, we make use of the sine law to get the angle, B, which is opposite to the side B. The sine law results to the formula: sin(A)/a = sin(B)/b and consequently, sin(75)/8.6691 = sin(B)/8. We then get B = 63.0464°. However, the direction of the resultant vector is given by the angle Θ which is Θ = 90° - 63.0464° = 26.9536°.
In summary, the resultant vector has a magnitude of 8.6691 m and it makes an angle equal to 26.9536° with the x-axis.
The heat capacity is given by the expression:
When the 
is measured in the calorimeter, we obtain a value, and since we know the mass of the material and we control the change in 
, we can then determine the specific heat "C" by simply remplazing in the expression.
Coefficient of volume expansion is 8.1 ×10⁻⁴ C⁻¹.
<u>Explanation:</u>
The volume expansion of a liquid is given by ΔV,
ΔV = α V₀ ΔT
ΔT = change in temperature = 48.5° C
α = coefficient of volume expansion =?
V₀ = initial volume = 2.35 m³
We need to find α , by plugin the given values in the equation and by rearranging the equation as,
= 8.1 ×10⁻⁴ C⁻¹.
Answer:
The angular displacement of the wheel is 45 radians
Explanation:
Given;
initial angular velocity, ω₀ = 20 rad/s
final angular velocity, ωf = 10 rad/s
time interval, t = 5
Angular acceleration is calculated as;
|α| = 2 rad/s²
Angular displacement is calculated as;
Therefore, the angular displacement of the wheel is 45 radians
