A car $$2$$ m long and $$3m$$ wide is moving at $$10$$ $$m/s$$ when a bullet hits it in a direction making an angle of $$tan$$$$-1(34)$$ with the car as seen from the ground. The bullet enters one edge of the car at the corner and passes out at diagonally opposite corner. Neglecting gravity, the time for the bullet to cross the car is

Question

A car $$2$$ m long and $$3m$$ wide is moving at $$10$$ $$m/s$$ when a bullet hits it in a direction making an angle of $$tan$$$$-1(34)$$ with the car as seen from the ground. The bullet enters one edge of the car at the corner and passes out at diagonally opposite corner. Neglecting gravity, the time for the bullet to cross the car is

Infinity Learn · Accepted Answer

Let the speed of bullet be v. The component of relative velocity in the direction of the length of the car is v $$cos$$ θ $$-$$ $$10$$ and in the direction of the width of the car is v $$sin$$ θ. Then from s $$=$$ $$vt.2$$ $$=(v$$ $$cos$$ θ $$-$$ $$10)$$ t and $$3$$ $$=$$ $$(v$$ $$sin$$ θ$$)tEliminating$$ v, we get t $$=$$ $$0.2$$ s

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