Please Provide Step by Step Solution :) A cannonball is shot forward to the sout

Question

Please Provide Step by Step Solution :)

A cannonball is shot forward to the southwest from the origin, starting at 120 m/s with an angle to the vertical phi = pi/6. Let the southwest be the angle theta = 5pi/4 in the xy-plane. Use the constant g = -10m/s2 for gravity (which is acceleration). What is the (3D) acceleration a(t) vector (in vector form)? Find the x,y,z components of the initial velocity vector v(0) (Hint: Use spherical coordinates). What is the (3D) velocity vector v(t)? If you were not able to find the acceleration vector in part (a), use a = (ax,ay. -az) where ax,ay,az are constants. If you did not find the initial velocity vector in part (b), use v0 = {vx(0), vy(0), vz(0)) where vx(0),vy(0),vz(0) are constants. What is the (3D) position vector r(t)? If you were not able to find the velocity vector, write the position in terms of the initial velocity vo and the acceleration a(t).

Explanation / Answer

4.)

a)
3D acceleration vector
there is no acceleration in x , y direction and in z direction we have an acceleration of g = -10 m/s^2
so 3D acceleration vector = a(t) = 0 i + 0 j -10 k = -10 k m/s^2

b)
South is negative y - axis and west be negative x - axis.
we have ? = 5?/4 , ? = ?/6
Initial velocity vector = 120 * sin ? *cos ? i + 120 * sin ? *sin ? j + 120 cos ? k
Initial velocity vector = 120 * sin ?/6 *cos 5?/4 i + 120 * sin ?/6 *sin 5?/4 j + 120 cos ?/6 k
Initial velocity vector = 1.094 i + 0.0751 j + 119.9949 k
x component of initial velocity = 1.094 m/s
y component of initial velocity = 0.0751 m/s
z component of initial velocity = 119.9949 m/s

c)
3D velocity vector
Vi is initial velocity vector.
velocity = V i + ( a * t) = (1.094 i + 0.0751 j + 119.9949 k ) - ( 10*t k)
3D velocity vector ,v(t) = 1.094 i + 0.0751 j + (119.9949- (10*t)) k
V(t) = (Vx(0) i + Vy(0) j + Vz(0) - az*t k)

d) position vector r(t) = int ( 0 to t) ( V dt)
r(t) = int ( 0 to t) ( 1.094 i + 0.0751 j + (119.9949- (10*t)) k dt)
r(t) = 1.094*t i + 0.0751*t j + (119.9949*t - (5*t^2)) k
r(t) = (Vx(0)*t i + Vy(0)*t j + Vz(0)*t - (az*t^2)/2 k)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---