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.
Answer:
Fr = 26.83 [N]
Explanation:
To solve this problem we must use the Pythagorean theorem, since the forces are vector quantities, that is, they have magnitude and density. Therefore the Pythagorean theorem is suitable for the solution of this problem.
![F_{r}=\sqrt{(12)^{2}+(24)^{2} } \\F_{r}=26.83[N]](https://tex.z-dn.net/?f=F_%7Br%7D%3D%5Csqrt%7B%2812%29%5E%7B2%7D%2B%2824%29%5E%7B2%7D%20%20%7D%20%5C%5CF_%7Br%7D%3D26.83%5BN%5D)
Answer:
769,048.28Joules
Explanation:
A parachutist of mass 56.0 kg jumps out of a balloon at a height of 1400 m and lands on the ground with a speed of 5.10 m/s. How much energy was lost to air friction during this bump
The energy lost due to friction is expressed using the formula;
Energy lost = Potential Energy + Kinetic Energy
Energy lost = mgh + 1/2mv²
m is the mass
g is the acceleration due to gravity
h is the height
v is the speed
Substitute the given values into the formula;
Energy lost = 56(9.8)(1400) + 1/2(56)(5.10)²
Energy lost = 768,320 + 728.28
Energy lost = 769,048.28Joules
<em>Hence the amount of energy that was lost to air friction during this jump is 769,048.28Joules</em>
Answer:
to the right
Explanation:
The balls collide in a completely inelastic collision, in other words they have the same velocity after the collision, this velocity has a magnitude V.
We need to use the conservation of momentum Law, the total momentum is the same before and after the collision.
In the axis X:
(1)
It is false. The effect of freezing is almost the exact opposite
