please help Two tanks are engaged in a training exercise on level ground. The fi

Question

please help

Two tanks are engaged in a training exercise on level ground. The first tank fires a paint-filled training round with a muzzle speed of 260m/s at an angle 13.0degree above the horizontal while advancing toward the second tank with a speed of 14.0m/s relative to the ground. The second tank is retreating at a speed of 35.5m/s relative to the ground, but is hit by the shell. You can ignore air resistance and assume the shell hits at the same height above ground from which it was fired. Find the distance between the tanks when the round was first fired. Find the distance between the tanks at the time of impact.

Explanation / Answer

Let the distance be x between tanks when round was fired

Horizontal distance covered by tank 1 =v_x* time of flight

v_x = 260*cos(theta) + 14

S_1= [260*cos(theta) + 14] * [2*260*sin(theta)/g] = 3187.72 m

Distance covered by tank 2 in same time =

S_2 = 35.5*[2*260*sin(theta)/g] = 423.3 m

x = S_1- S_2 = 2764.42 m

let y be the distance between them at the time of impact

S_1' = 14*[2*260*sin(theta)/g] = 14*11.92 = 166.88m

S_2' = 35.5*[2*260*sin(theta)/g] = 35.5*11.92 = 423.3 m

y = S_2' - S_1' +x = 3020.84 m

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