Answer to Question #300461 in Mechanics | Relativity for Tobi

Question

A French mortar fires a projectile at an angle of 45° to horizontal with a muzzle velocity of 200m/s. A tank is advancing direct towards the mortar on a level ground at a speed of 10m/s. What should be the distance from the mortar to the tank at the instant thr mortar is fired in order to score a direct hit?

Answer 1

Explanations & Calculations

• The vertical velocity component of the mortar is $\small 200 \sin45 = 141.4\,ms^{-1}$
• Then the time of flight is

$\qquad\qquad \begin{aligned} \small \uparrow s&=\small ut +\frac{1}{2}at^2\\ \small 0&=\small 141.4t-4.9t^2\\ \small t&=\small 0s \qquad t=28.9\,s \end{aligned}$

• Its horizontal velocity is $\small 200\cos45=141.4\,ms^{-1}$ (say to right $\small \to$ ).
• Now, the easiest method is to consider the relative velocities, take the horizontal velocity of the mortar relative to the tank (stop the tank and add its velocity to the mortar's),

$\small 141.4(\to)+10(-\leftarrow ) = 151.4\,ms^{-1}$

• Then the distance should be

$\qquad\qquad \begin{aligned} \small S&=\small ut\\ &=\small 151.4\,ms^{-1}\times 28.9\,s\\ &=\small 4375.5\,m \end{aligned}$

• So there should be that distance in between before the mortar is fired.