Question

An artillery shell is fired with an initial velocity of 250 m/s at 50.0° above the horizontal. After a period of 40.0 seconds from firing, it explodes on a mountainside.



What is the y- coordinate of the impact site relative to the firing point?

Answer 1

Let us put the axes origin to a place where the artillery shell was fired from. Then the law of motion for the shell along the y-axis can be written as:

$$y(t)=v_0 t \sin{\alpha} - \frac{g t^2}{2}$$

Substituting the numerical values, we obtain:

$$y = 250 \cdot 40 \cdot \sin{50}-\frac{10 \cdot 40^2}{2} \approx -340 \, m$$

Answer: the y-coordinate is 340 m below the firing point.