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A projectile is fired at a speed of 100 m/s at an angle of 37^(@) above the horizontal. At the highest point, the projectile breaks into two parts of mass ratio 1 : 3, the smaller piece coming to rest. Find the distance from the launching point to the point where the heavier piece lands.

Answer» <html><body><p></p>Solution :Internal forces do not affect the motion of the centre of mass, the centre of mass <a href="https://interviewquestions.tuteehub.com/tag/hits-1028215" style="font-weight:bold;" target="_blank" title="Click to know more about HITS">HITS</a> the ground at a position where the original projectile would have landed. The range of the original projectile is<br/><img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_DOC_OBJ_PHY_XI_V01_B_C07_SLV_018_S01.png" width="80%"/><br/>`X_(CM)=(<a href="https://interviewquestions.tuteehub.com/tag/2u-301178" style="font-weight:bold;" target="_blank" title="Click to know more about 2U">2U</a>^(2)sin theta <a href="https://interviewquestions.tuteehub.com/tag/cos-935872" style="font-weight:bold;" target="_blank" title="Click to know more about COS">COS</a> theta)/(g)=(2xx10^(4)xx(3)/(5)xx(4)/(5))/(10)m=960m`<br/>The centre of mass will hit the ground at this position. As the <a href="https://interviewquestions.tuteehub.com/tag/smaller-1213327" style="font-weight:bold;" target="_blank" title="Click to know more about SMALLER">SMALLER</a> block comes to rest after breaking, it falls down vertically and hits the ground at <a href="https://interviewquestions.tuteehub.com/tag/half-1014510" style="font-weight:bold;" target="_blank" title="Click to know more about HALF">HALF</a> of the range, i.e., at x = 480 m. If the heavier block hits the ground at `x_(2)`, then <br/>`X_(CM)=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))rArr 960 =((m)(480)+(3m)(x_(2)))/((m+3m))`<br/>`therefore x_(2)=1120m`</body></html>


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