You are serving as a consultant for the newest James bond film. In one scene the

Question

You are serving as a consultant for the newest James bond film. In one scene the, Bond must fire a projectile from a cannon and hit the enemy headquarters located on the top of a cliff 62m above and 319m from the cannon. The cannon will shoot the projectile at an angle of 39 degrees above the horizontal. The director wants to know what the speed of the projectile must be when it is fired from the cannon so that it will hit the enemy headquarters. What do you tell him?

The firing speed v initial= ______m/s

Explanation / Answer

let v be the required speed of the cannon

then horizontal disatnce travelled is X = 319 m

but X = v*cos(39)*t = 319

t = 319/(v*cos(39)).....(1)

and vertical distance travelled in t seconds is y = 62 m

y = (v*sin(39)*t) -(0.5*g*t^2)...(2)

62= (v*sin(39)*t)-(0.5*9.81*t^2)

substituting (1) in (2) we get

62 = (v*sin(39)*319/(v*cos(39))) - (4.9*319*319/(v^2*cos^2(39)))

62 = 258.32 - 825604.9/v^2

825604.9/v^2 = 196.32

v = 64.84 m/s

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