Find the distance between the tanks when the round was first fired. Find the dis

Question

Find the distance between the tanks when the round was first fired.

Find the distance between the tanks at the time of impact.

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 246 m/s at an angle 12.6° above the horizontal while advancing toward the second tank with a speed of 15.0 m/s relative to the ground. The second tank is retreating at a speed of 35.5 m/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.

Explanation / Answer

Given,

v0 = 246 m/s ; theta= 12.6 deg

v0y = 246 sin12.6 = 53.66

v0x = 246 cos12.6 = 240.08 m/s

so for the time, it will go on,

t = 53.66/9.8 = 5.48 s

Total time of flight = 2t = 2 x 5.48 = 10.96 s

range is:

D = v0x t = 240.08 c 10.96 = 2631.28 m

Hence, D = 2631.28 m

b)v' = 35.5 - 15 = 20.5 m/s

so, D now will be:

D = 20.5 x 10.96 = 224.68 m

d = 2631.28 - 224.68 = 2406.7 m

So at impact

Hence, d = 2406.7 m

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