{"id":681669,"date":"2023-09-03T10:34:09","date_gmt":"2023-09-03T05:04:09","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-man-is-watching-from-the-top-of-a-tower-a-boat-speeding-away-from-the-tower-the-boat-makes-an-angle-of-depression-of-450with-the-mans-eye-when-at-a-distance-of-60-meters-from-the-tower-after-5\/"},"modified":"2025-06-20T13:27:10","modified_gmt":"2025-06-20T07:57:10","slug":"a-man-is-watching-from-the-top-of-a-tower-a-boat-speeding-away-from-the-tower-the-boat-makes-an-angle-of-depression-of-450with-the-mans-eye-when-at-a-distance-of-60-meters-from-the-tower-after-5","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/a-man-is-watching-from-the-top-of-a-tower-a-boat-speeding-a\/","title":{"rendered":"A man is watching from the top of a tower, a boat speeding away from the tower. The boat makes an angle of depression of 450with the man’s eye when at a distance of 60 meters from the tower. After 5 seconds the angle of depression becomes 300. What is the approximate speed of the boat assuming that it is running in still water?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A man is watching from the top of a tower, a boat speeding away from the tower. The boat makes an angle of depression of 450with the man's eye when at a distance of 60 meters from the tower. After 5 seconds the angle of depression becomes 300. What is the approximate speed of the boat assuming that it is running in still water?","custom_permalink":"question\/mathematics\/a-man-is-watching-from-the-top-of-a-tower-a-boat-speeding-a\/"},"categories":[],"acf":{"question":"

A man is watching from the top of a tower, a boat speeding away from the tower. The boat makes an angle of depression of <\/span>45<\/mn><\/mrow>0<\/mn><\/mrow><\/msup><\/math>with the man's eye when at a distance of 60 meters from the tower. After 5 seconds the angle of depression becomes <\/span>30<\/mn><\/mrow>0<\/mn><\/mrow><\/msup><\/math>. What is the approximate speed of the boat assuming that it is running in still water? <\/span><\/p>

<\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\">","options":[{"option":"30km\/h<\/span>","correct":false},{"option":"40km\/h<\/span>","correct":false},{"option":"32km\/h<\/span>","correct":true},{"option":"45km\/h<\/span> <\/span>","correct":false}],"solution":"Given that,<\/span>
AC<\/mi>=<\/mo>60<\/mn> m<\/mi><\/math> <\/span> <\/span>\u2220<\/mo>ADB<\/mi>=<\/mo>30<\/mn><\/mrow>0<\/mn><\/mrow><\/msup><\/math>
\u2220<\/mo>ACB<\/mi>=<\/mo>45<\/mn><\/mrow>0<\/mn><\/mrow><\/msup><\/math> <\/span>\"\"We have the formula,<\/span>
tan\u03b8<\/mi>=<\/mo>Height<\/mi><\/mrow>Distance<\/mi><\/mrow><\/mfrac><\/math> <\/span>We have to find the speed of the boat,<\/span>
AB<\/mi><\/math> is the tower, <\/span>
C<\/mi><\/math>and <\/span>D<\/mi><\/math> are the point of observation from the boat. <\/span>
Taking the height of tower as h meters,<\/span>
In <\/span>\u0394BAC<\/mi><\/math>,<\/span>
 <\/span>tan<\/mi>45<\/mn><\/mrow>0<\/mn><\/mrow><\/msup>=<\/mo>AB<\/mi><\/mrow>AC<\/mi><\/mrow><\/mfrac><\/math> <\/span>\u21d2<\/mo>1<\/mn>=<\/mo>AB<\/mi><\/mrow>60<\/mn><\/mrow><\/mfrac><\/math> <\/span>\u21d2<\/mo>AB<\/mi>=<\/mo>60<\/mn> m<\/mi><\/math> <\/span>In <\/span>\u0394BAD<\/mi><\/math>, <\/span>
tan<\/mi>30<\/mn><\/mrow>o<\/mi><\/mrow><\/msup>=<\/mo>AB<\/mi><\/mrow>AD<\/mi><\/mrow><\/mfrac><\/math> <\/span> <\/span>\u21d2<\/mo>1<\/mn><\/mrow>3<\/mn><\/mrow><\/msqrt><\/mrow><\/mfrac>=<\/mo>60<\/mn><\/mrow>AD<\/mi><\/mrow><\/mfrac><\/math> <\/span>\u21d2<\/mo>AD<\/mi>=<\/mo>60<\/mn>3<\/mn><\/mrow><\/msqrt> m<\/mi><\/math> <\/span> <\/span>\u2234<\/mo>CD<\/mi>=<\/mo>AD<\/mi>-<\/mo>AC<\/mi><\/math>
\u21d2<\/mo>CD<\/mi>=<\/mo>60<\/mn>3<\/mn><\/mrow><\/msqrt>-<\/mo>60<\/mn><\/math> <\/span>\u21d2<\/mo>CD<\/mi>=<\/mo>60<\/mn>(<\/mo>3<\/mn><\/mrow><\/msqrt>-<\/mo>1<\/mn>)<\/mo><\/math> <\/span>Then, speed, s <\/span>=<\/mo>60<\/mn>(<\/mo>3<\/mn><\/mrow><\/msqrt>-<\/mo>1<\/mn>)<\/mo><\/mrow>5<\/mn><\/mrow><\/mfrac> m<\/mi>\/<\/mo>s<\/mi><\/math>.<\/span>
The approximate speed will be,<\/span>
s<\/mi>=<\/mo>12<\/mn>\u00d7<\/mo>0<\/mn>.<\/mo>73<\/mn>\u00d7<\/mo>3600<\/mn><\/mrow>1000<\/mn><\/mrow><\/mfrac><\/math>       <\/span>(1<\/span>m<\/mi>\/<\/mo>s<\/mi>=<\/mo>3600<\/mn><\/mrow>1000<\/mn><\/mrow><\/mfrac>km<\/mi>\/<\/mo>h<\/mi>)<\/mo><\/math>
\u21d2<\/mo><\/math>s=31.536<\/span>
\u21d2<\/mo>s<\/mi>\u2248<\/mo>32<\/mn> km<\/mi>\/<\/mo>h<\/mi><\/math> <\/span>Thus the approximate speed is 32km\/h.<\/span>
Therefore the correct option is 3.<\/span>
 <\/span>","subject":"Mathematics"},"yoast_head":"\nA man is watching from the top of a tower, a boat speeding away from the tower. The boat makes an angle of depression of 450with the man's eye when at a distance of 60 meters from the tower. After 5 seconds the angle of depression becomes 300. What is the approximate speed of the boat assuming that it is running in still water? - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"A man is watching from the top of a tower, a boat speeding away from the tower. The boat makes an angle of depression of 450with the man's eye when at a distance of 60 meters from the tower. After 5 seconds the angle of depression becomes 300. 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