$(35$ Points$)$ Both the pressure rise $(P)$ across a blast wave and the speed of the wind induced behind the wave $(V)$ is assumed to be a function of the energy released in the explosion $(E),$ the air density $(),$ the peed of sound in the air behind the wave $(c),$ and the istance from the blast $($d$).$

$(17$ Points$)$ Solve for all the relevant $$ groups using $(c),(d),$ and one other variable as the repeating parameters.

$9$ Points$)$ Consider two blasts. The prototype blast is $1500$ times larger than the odel blast, and both take place in the same initial STP $($standard temperature and essure$)$ air. At what distance from the model blast will the pressure rise be the s: hat at a distance of $5$ km from the prototype blast?

oints$)$ At a location of $70$ m from the model blast the wind moves at $V=260$ is the wind speed for the prototype at a distance of $7\mathrm{.}5$ km from the blast$$xs n