Answer:
a) v₃ = 19.54 km, b) 70.2º north-west
Explanation:
This is a vector exercise, the best way to solve it is finding the components of each vector and doing the addition
vector 1 moves 26 km northeast
let's use trigonometry to find its components
cos 45 = x₁ / V₁
sin 45 = y₁ / V₁
x₁ = v₁ cos 45
y₁ = v₁ sin 45
x₁ = 26 cos 45
y₁ = 26 sin 45
x₁ = 18.38 km
y₁ = 18.38 km
Vector 2 moves 45 km north
y₂ = 45 km
Unknown 3 vector
x3 =?
y3 =?
Vector Resulting 70 km north of the starting point
R_y = 70 km
we make the sum on each axis
X axis
Rₓ = x₁ + x₃
x₃ = Rₓ -x₁
x₃ = 0 - 18.38
x₃ = -18.38 km
Y Axis
R_y = y₁ + y₂ + y₃
y₃ = R_y - y₁ -y₂
y₃ = 70 -18.38 - 45
y₃ = 6.62 km
the vector of the third leg of the journey is
v₃ = (-18.38 i ^ +6.62 j^ ) km
let's use the Pythagorean theorem to find the length
v₃ = √ (18.38² + 6.62²)
v₃ = 19.54 km
to find the angle let's use trigonometry
tan θ = y₃ / x₃
θ = tan⁻¹ (y₃ / x₃)
θ = tan⁻¹ (6.62 / (- 18.38))
θ = -19.8º
with respect to the x axis, if we measure this angle from the positive side of the x axis it is
θ’= 180 -19.8
θ’= 160.19º
I mean the address is
θ’’ = 90-19.8
θ = 70.2º
70.2º north-west
Answer:
S = 11.025 m
Explanation:
Given,
The time taken by the pebble to hit the water surface is, t = 1.5 s
Acceleration due to gravity, g = 9.8 m/s²
Using the II equations of motion
S = ut + 1/2 gt²
Here u is the initial velocity of the pebble. Since it is free-fall, the initial velocity
u = 0
Therefore, the equation becomes
S = 1/2 gt²
Substituting the given values in the above equation
S = 0.5 x 9.8 x 1.5²
= 11.025 m
Hence, the distance from the edge of the well to the water's surface is, S = 11.025 m
Answer:
57.6Joules
Explanation:
Rotational kinetic energy of a body can be determined using the expression
Rotational kinetic energy = 1/2Iω²where;
I is the moment of inertia around axis of rotation. = 5kgm/s²
ω is the angular velocity = ?
Note that torque (T) = I¶ where;
¶ is the angular acceleration.
I is the moment of inertia
¶ = T/I
¶ = 3.0/5.0
¶ = 0.6rad/s²
Angular acceleration (¶) = ∆ω/∆t
∆ω = ¶∆t
ω = 0.6×8
ω = 4.8rad/s
Therefore, rotational kinetic energy = 1/2×5×4.8²
= 5×4.8×2.4
= 57.6Joules
Transverse wave as the wave is going up and down no compressions
Answer:
The young tree, originally bent, has been brought into the vertical position by adjusting the three guy-wire tensions to AB = 7 lb, AC = 8 lb, and AD = 10 lb. Determine the force and moment reactions at the trunk base point O. Neglect the weight of the tree.
C and D are 3.1' from the y axis B and C are 5.4' away from the x axis and A has a height of 5.2'
Explanation:
See attached picture.