Question

An artillery shell is fired with an initial speed of 300m/s at 55 deegry about the horizontal,it explodes on a mountain side 42s after firing,what are the x and y coordinate of the shell where it explodes relative to its firing point?

Answer 1

x = 7226.94 m

y = 1677.4 m

Step-by-step explanation:

This is a classic problem of a parabolic move. Let's analyze the given data.

The speed is 300 m/s but it's fired at 55°, so the x and y component of the speed would be:

Vx = 300 cos55 = 172.07 m/s

Vy = 300 sin55 = 245.75 m/s

Now, to get the x and y components of the shell, we need to apply the following expressions:

X = Xo + Vx*t (1)

Y = Yo + Vy*t - 1/2 gt² (2)

Xo and Yo is 0, and we already have the speed in x and y, so the components are:

X = 0 + (172.07)(42)

X = 7226.94 m

For the y component:

Y = 0 + (245.75)(42) - 1/2 (9.8)(42)²

Y = 10321.5 - 8643.6

Y = 1677.4 m

Hope this helps