{"id":247169,"date":"2022-09-10T09:17:16","date_gmt":"2022-09-10T03:47:16","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-particle-of-mass-m-is-projected-with-velocity-v-making-an-angle-of-45-with-the-horizontal-when-the-particle-lands-on-the-level-ground-the-magnitude-of-the-change-in-its-momentum-will-be\/"},"modified":"2022-12-14T15:49:05","modified_gmt":"2022-12-14T10:19:05","slug":"question-physics-a-particle-of-mass-m-is-projected-with-velocity-v-making-an","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-of-mass-m-is-projected-with-velocity-v-making-an\/","title":{"rendered":"A particle of mass m is projected with velocity v making an angle of 45\u00b0 with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be:"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"a particle of mass m is projected with velocity v","_yoast_wpseo_title":"A Particle of Mass m is Projected with Velocity v Making an Angle of 45\u00b0","_yoast_wpseo_metadesc":"A Particle of mass m is projected with velocity v making an angle of 45\u00b0 with the horizontal. infinitylearn.com.","custom_permalink":"question\/physics\/a-particle-of-mass-m-is-projected-with-velocity-v-making-an\/"},"categories":[],"acf":{"question":"

A particle of mass m is projected with velocity v making an angle of 45\u00b0 with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be:<\/p>","options":[{"option":"

2mv<\/p>","correct":false},{"option":"

m<\/mi>v<\/mi><\/mrow>2<\/mn><\/msqrt><\/mfrac><\/math><\/p>","correct":false},{"option":"

mv<\/mi>2<\/mn><\/msqrt><\/math><\/p>","correct":true},{"option":"

zero<\/p>","correct":false}],"solution":"

The magnitude of the resultant velocity at the point of projection and the landing point is same.<\/p>

<\/figure>

Clearly, change in momentum along horizontal (i.e along x-axis)<\/p>

=<\/mo>m<\/mi>v<\/mi>cos<\/mi>\u03b8<\/mi>-<\/mo>m<\/mi>v<\/mi>cos<\/mi>\u03b8<\/mi>=<\/mo>0<\/mn><\/math><\/p>

Change in momentum along vertical (i.e. along y\u2013axis) =<\/p>

m<\/mi>v<\/mi>sin<\/mi>\u03b8<\/mi>-<\/mo>(<\/mo>-<\/mo>m<\/mi>v<\/mi>sin<\/mi>\u03b8<\/mi>)<\/mo><\/math><\/p>

=<\/mo>2<\/mn>m<\/mi>v<\/mi>sin<\/mi>\u03b8<\/mi>=<\/mo>2<\/mn>m<\/mi>v<\/mi>\u00d7<\/mo>sin<\/mi>45<\/mn>\u00b0<\/mo><\/math><\/p>

=<\/mo>2<\/mn>mv<\/mi>\u00d7<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac>=<\/mo>2<\/mn><\/msqrt>mv<\/mi><\/math><\/p>

Hence, resultant change in momentum =<\/mo>2<\/mn><\/msqrt>mv<\/mi><\/math><\/p>","subject":""},"yoast_head":"\nA Particle of Mass m is Projected with Velocity v Making an Angle of 45\u00b0<\/title>\n<meta name=\"description\" content=\"A Particle of mass m is projected with velocity v making an angle of 45\u00b0 with the horizontal. infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-of-mass-m-is-projected-with-velocity-v-making-an\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A Particle of Mass m is Projected with Velocity v Making an Angle of 45\u00b0\" \/>\n<meta property=\"og:description\" content=\"A Particle of mass m is projected with velocity v making an angle of 45\u00b0 with the 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