Question

An artillery shell is fired with an initial velocity of 300 m/s at 55.0° above the horizontal. It explodes on a mountainside 42.0 s after firing. If x is horizontal and y vertical, find the (x, y) coordinates where the shell explodes.

Answer 1

Answer:

x=7227

y=1678

(7227,1678)

Explanation:

Ok, check the picture I attached you, because of the problem don't give us aditional information, let's asume that the projectile is fired from an initial position x=0 and y=0. Now let's use projectile motion equations, but firs let's find the initial velocity components in x-axis and y-axis:

$v_ox=v_o*cos(\theta_o)=300*cos(55)=172.0729309m/s$

$v_oy=v_o*sin(\theta_o)=300*sin(55)=245.7456133m/s$

Now, let's find the x coordinate with this equation:

$x-x_o=x-0=x=v_ox*t=172.0729309*42=7227.063098m$

Finally asumming a gravity constant g=9.8, let's find the y coordinate with the next equation:

$y-y_o=y-0=y=v_oy*t-\frac{1}{2}*g*t^{2} =(245.7456133*42)-\frac{42^{2} *9.8}{2}$

$y=10321.31576-8643.6=1677.71576m$