A-8. WISE UNUN) A gun kept on a str...

A-8. WISE UNUN) A gun kept on a straight horizontal road is used to hit a car, travelling along the same road away from the gun with a uniform speed of 72 x 12 km/hour. The car is at a distance of 50 metre from the gun, when the gun is fired at an angle of 45° with the horizontal. Find (i) the distance of the car from the gun when the shell hits it, (ii) the speed of projection of the shell from the gun. (g = 10 m/s?] [IIT 1974)

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So, Initial speed of bullet be 'v'. ( t=frac{2 v sin (theta)}{g} ) 2) We also observe that, Speed of car, ( u=72 sqrt{2} mathrm{km} / mathrm{h}=2 mathrm{O} sqrt{2} mathrm{m} / mathrm{s} ) Distance covered by car Range of Projectile ( =50 mathrm{m}+20 sqrt{2}^{*} mathrm{t} ) ( =>frac{v^{2} sin (2 times 45)}{g}=50+20 sqrt{2}left(frac{2 v sin (45)}{g}right) ) ( =>v^{2}-40 v-500=0 ) ( =>(v-50)(v+10)=0 ) ( =>v=50 quad(v eq-10) ) (b) Hence, Speed of Projection of shell ( =50 mathrm{m} / mathrm{s} ) (a) Distance from the gun: Range of Projectile: ( =frac{v^{2} sin (2 times 45)}{g}=frac{50^{2} times 1}{10}=250 mathrm{m} ) Hence, Distance from gun ( =250 mathrm{m} )
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