{"id":340307,"date":"2023-01-06T11:31:31","date_gmt":"2023-01-06T06:01:31","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-stone-is-dropped-from-a-roof-how-much-time-does-it-take-to-fall-4-9-m-takeg-9-8-m-s2\/"},"modified":"2025-06-26T18:21:38","modified_gmt":"2025-06-26T12:51:38","slug":"a-stone-is-dropped-from-a-roof-how-much-time-does-it-take-to-fall-4-9-m-takeg-9-8-m-s2","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-stone-is-dropped-from-a-roof-how-much-time-does-it-take-t\/","title":{"rendered":"A stone is dropped from a roof. How much time does it take to fall 4.9\u00a0m? (Takeg\u00a0=\u00a09.8\u00a0m\/s2)."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A stone is dropped from a roof. How much time does it take to fall 4.9\u00a0m? (Takeg\u00a0=\u00a09.8\u00a0m\/s2).","custom_permalink":"question\/physics\/a-stone-is-dropped-from-a-roof-how-much-time-does-it-take-t\/"},"categories":[],"acf":{"question":"

A stone is dropped from a roof. How much time does it take to fall <\/span>4<\/mn>.<\/mo>9<\/mn> m<\/mi><\/math>? (Take<\/span>g <\/mi>=<\/mo> <\/mi>9<\/mn>.<\/mo>8<\/mn> m<\/mi>\/<\/mo>s<\/mi><\/mrow>2<\/mn><\/mrow><\/msup><\/math>).<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:8pt;line-height:normal;font-size:12pt\"><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:8pt;line-height:normal;font-size:12pt\">","options":[{"option":"1<\/mn> s<\/mi><\/math>","correct":true},{"option":"2<\/mn> s<\/mi><\/math>","correct":false},{"option":"3<\/mn> s<\/mi><\/math>","correct":false},{"option":"4<\/mn> s<\/mi><\/math> <\/span>","correct":false}],"solution":" <\/span>A stone is dropped from a roof of height <\/span>4<\/mn>.<\/mo>9<\/mn> m<\/mi><\/math>. The time taken to fall is <\/span>1<\/mn> s<\/mi>.<\/mo><\/math>
As the stone is dropped, the initial velocity is <\/span>0<\/mn> m<\/mi>\/<\/mo>s<\/mi><\/math>. The acceleration of the stone is the acceleration due to gravity <\/span>(<\/mo>g<\/mi>)<\/mo><\/math> in the downward direction.<\/span>
So, initial velocity <\/span>(<\/mo>u<\/mi>)<\/mo> <\/mi>=<\/mo>0<\/mn> m<\/mi>\/<\/mo>s<\/mi><\/math>
Acceleration <\/span> <\/mi>(<\/mo>a<\/mi>)<\/mo> <\/mi>=<\/mo>9<\/mn>.<\/mo>8<\/mn> m<\/mi>\/<\/mo>s<\/mi><\/mrow>2<\/mn><\/mrow><\/msup><\/math>                                <\/span>acceleration a will be equal to <\/span>g<\/mi><\/math> (acceleration due to gravity) in the state of free-falling<\/span>
Distance travelled <\/span> <\/mi>(<\/mo>s<\/mi>)<\/mo> <\/mi>=<\/mo>4<\/mn>.<\/mo>9<\/mn> m<\/mi><\/math>
Applying the equation of motion <\/span>s <\/mi>=<\/mo> ut <\/mi>+<\/mo> <\/mi>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac> a<\/mi>t<\/mi><\/mrow>2<\/mn><\/mrow><\/msup><\/math>
Putting the values<\/span>
 <\/span>\u21d2<\/mo>4<\/mn>.<\/mo>9<\/mn> <\/mi>=<\/mo> <\/mi>0<\/mn> <\/mi>+<\/mo> <\/mi>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac>\u00d7<\/mo> <\/mi>9<\/mn>.<\/mo>8<\/mn> <\/mi>\u00d7<\/mo> <\/mi>t<\/mi><\/mrow>2<\/mn><\/mrow><\/msup><\/math>
 <\/span>\u21d2<\/mo>t<\/mi><\/mrow><\/mrow><\/msub>=<\/mo> <\/mi>2<\/mn>\u00d7<\/mo>4<\/mn>.<\/mo>9<\/mn><\/mrow>9<\/mn>.<\/mo>8<\/mn><\/mrow><\/mfrac><\/mrow><\/msqrt><\/math> <\/span> <\/span>\u21d2<\/mo>t<\/mi><\/mrow><\/mrow><\/msub>=<\/mo> <\/mi>1<\/mn> s<\/mi><\/math>.<\/span>
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