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 86.0  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 143.0  m high; the base of the cliff is 175.0  m to the east of the cannon.

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.

Give your answers as an ordered triple, with the x position at 2.0 seconds first, followed by a comma, followed by the x position at 4.0 seconds, followed by a comma, followed by the x position at 6.0 seconds.

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.

Give your answers as an ordered triple, with the y position at 2.0 seconds first, followed by a comma, followed by the y position at 4.0 seconds, followed by a comma, followed by the y position at 6.0 seconds.

Answer 1

The x equation can be written as

x = x_o + v_xt + 1/2a_xt²

as there is no acceleration in x direction, our equation becomes.

x = v_xt

so,

at t = 2 sec

x = 86 * cos 51 * 2

x = 108.24 m

at t = 4 sec

x = 216.48 m

at t = 6

x = 324.7 m

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Now, writing the y equation

y = v_yt - 1/2gt²

so,

at t = 2

y = 86 * sin 51 * 2 - 1/2 * 9.8 * 4

y = 114.1 m

at t = 4

y = 189 m

at t = 6

y = 224.6 m