Question

A restored Civil War cannon is being tested using cannonballs of various mass and using various loads of gunpowder. In one test, the cannon fires a cannonball at a speed of 74.0  m/s in a direction which is 51.0  degrees Up from East. The cannonball is intended to land on a mesa which is to the east of the cannon. The near edge of the mesa is a vertical cliff which is 103.0  m high; the base of the cliff is 127.0  m to the east of the cannon.

In answering the questions below, use an xy coordinate system with East as the positive x direction and Up as the positive y direction. I solved A-G, need help with H

A.) Find an equation for the x position of the cannonball as a function of time, taking t=0 to be the time of firing and taking x=0 at the firing location. Then give the x values for the three times requested.

x(2.0 s), x(4.0 s), x(6.0 s) =

93.1,186,279

m, m, m

B.) Find an equation for the y position of the cannonball as a function of time, taking t=0 to be the time of firing and taking y=0 at the firing location. Then give the y values for the three times requested.

y(2.0 s), y(4.0 s), y(6.0 s) =

95.4,152,169

m, m, m

C.) Solve for the two times during the flight of the cannonball when the altitude of the cannonball is 103.0  m . Enter the earliest time first.

early time, late time =

2.21,9.53

s, s

D.) Solve for the time when the cannonball is directly above the edge of the cliff, and also solve for the altitude of the cannonball at that time.

time, altitude

2.73,120

s, m

E.) Assuming the top of the mesa is perfectly horizontal, solve for the x position of the cannonball when it strikes the ground atop the mesa.

444

m

F.) Find an equation for the y velocity of the cannonball, and use that equation to find the y velocity at the following times. Indicate the direction of the y velocity with an appropriate plus or minus sign.

vy(2.0 s), vy(4.0 s), vy(6.0 s),

37.9,18.3,-1.29

m/s, m/s, m/s

G.) Use your equation for the y velocity of the cannonball to find the y velocity when the cannonball is passing over the cliff edge, and again just before the cannonball crashes into the ground.

30.8,-35.9

m/s, m/s

H.) Use the definition of angular momentum, in three dimensions, along with an equation for the position of the cannonball (as measured from the base of the cliff) and an equation for the velocity of the cannonball, to find an equation for the angular momentum of the cannonball as a function of time, as measured with respect to the point at the base of the cliff. Because your position and velocity vectors are all in the xy plane, your angular momentum vector (L⃗ ) will always be purely in the positive or negative z direction. Take South as the positive z direction (positive x is East and positive y is Up). Put your equation for Lz(t) into the following form: Mass cannon ball=3.9kg

Lz(t) = A + Bt + Ct2

and report your values of A, B, and C (some values may possibly be zero). Each term in your equation must have units of kg⋅m2/s.

Answer 1