Compute the components of the given vectors. Let
denote the plane's velocity vector, and
the wind. Then
![P=\langle P_x,P_y\rangle=\langle250\cos(-40^\circ),250\sin(-40^\circ)\rangle](https://tex.z-dn.net/?f=P%3D%5Clangle%20P_x%2CP_y%5Crangle%3D%5Clangle250%5Ccos%28-40%5E%5Ccirc%29%2C250%5Csin%28-40%5E%5Ccirc%29%5Crangle)
![\implies P=\langle191.5,-160.7\rangle](https://tex.z-dn.net/?f=%5Cimplies%20P%3D%5Clangle191.5%2C-160.7%5Crangle)
![W=\langle35\cos(-120^\circ),35\sin(-120^\circ)\rangle=\langle-17.5,-30.3\rangle](https://tex.z-dn.net/?f=W%3D%5Clangle35%5Ccos%28-120%5E%5Ccirc%29%2C35%5Csin%28-120%5E%5Ccirc%29%5Crangle%3D%5Clangle-17.5%2C-30.3%5Crangle)
The resultant velocity (rounded) is
![P+W=\langle174,-191\rangle](https://tex.z-dn.net/?f=P%2BW%3D%5Clangle174%2C-191%5Crangle)
with magnitude
and direction
, or about 258 mi/hr at 47.7 degrees south of east.
1.3s
Explanation:
Given parameters:
Height = 1.4m
Gravity on moon = 1.67ms⁻¹
Unknown:
Time for feather to fall = ?
Solution:
To solve this problem, we are going to use one of the motion equation that relates time, gravity and height.
H = ut + ![\frac{1}{2} g t^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20g%20t%5E%7B2%7D)
Sine the body was dropped from rest, initial velocity is zero;
H = height
u = initial velocity
t = time
g = acceleration due to gravity
since u = 0;
H = ![\frac{1}{2} g t^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20g%20t%5E%7B2%7D)
1.4 =
x 1.67 x t²
t = 1.3s
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Answer:
320N
Explanation:
The magnitude of the torque required is expressed using the formula;
T = Fr sin theta where;
F is the force
r is the radius = 9cm = 0.09m
theta is the angle of inclination = 8 degrees
Torque T = 4Nm
Substitute the given values and get F
4 = F(0.09)sin8
4 = 0.0125F
F = 4/0.0125
F = 320N
Hence the magnitude of the force required when the force is applied at 8 degrees to the wrench is 320N
Explanation:
using the formula: S=ut+½gt², where u=0, S=?, g=8m/s², t=10seconds.
S=ut+½gt² ("ut" term will cancel because u=0).
=> S= ½gt²
=>S = ½×8×10²
=>S = 4×100
=>S = 400m .
Therefore, the distance traveled by the body in 10s is 400m.
hope this helps you.