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Giải bài 7 trang 98 SGK Toán 10 tập 1 – Cánh diều

Một máy bay đang bay từ hướng đông sang hướng tây với tốc độ 700 km/h thì gặp luồng gió thổi từ hướng đông bắc sang hướng tây nam với tốc độ 40 km/h (Hình 68). Máy bay bị thay đổi vận tốc sau khi gặp gió thổi. Tìm tốc độ mới của máy bay (làm tròn kết quả đến hàng phần trăm theo đơn vị km/h.)

🏅Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Cánh diều

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Đề bài

Một máy bay đang bay từ hướng đông sang hướng tây với tốc độ 700 km/h thì gặp luồng gió thổi từ hướng đông bắc sang hướng tây nam với tốc độ 40 km/h (Hình 68). Máy bay bị thay đổi vận tốc sau khi gặp gió thổi. Tìm tốc độ mới của máy bay (làm tròn kết quả đến hàng phần trăm theo đơn vị km/h.)

Phương pháp giải - Xem chi tiết

+) Tổng hợp vecto vận tốc theo quy tắc hình bình hành: \(\overrightarrow {AB}  + \overrightarrow {AD}  = \overrightarrow {AC} \) (ABCD là hình bình hành) +) Định lí cosin trong tam giác ABC: \(A{C^2} = A{B^2} + B{C^2} - 2.AB.BC.\cos B\)

Lời giải chi tiết

Vẽ vecto \(\overrightarrow {AB} \) là vecto vận tốc của máy bay, \(\overrightarrow {AD} \) là vecto vận tốc của gió.Khi đó vecto vận tốc mới của máy bay là \(\overrightarrow {AB}  + \overrightarrow {AD} \)Dựng hình bình hành ABCD. Ta có: \(\overrightarrow {AB}  + \overrightarrow {AD}  = \overrightarrow {AC} \)Áp dụng định lí cosin trong tam giác ABC, ta có: \(A{C^2} = A{B^2} + B{C^2} - 2.AB.BC.\cos B\)Mà AB = 700, BC = AD = 40, \(\widehat B = {135^o}\)\(\begin{array}{l} \Rightarrow A{C^2} = {700^2} + {40^2} - 2.700.40.\cos {135^o} \approx 531197,98\\ \Leftrightarrow AC \approx 728,83\end{array}\)Vậy tốc độ mới của máy bay là 728,83 km/h.

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