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Bài 6 trang 15 SGK Toán 11 tập 1 - Cánh diều

Một vệ tinh được định vị tại vị trí A trong không gian.

༺Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Một vệ tinh được định vị tại vị trí A trong không gian. Từ vị trí A, vệ tinh bắt đầu chuyển động quanh Trái Đất theo quỹ đạo là đường tròn với tâm là tâm O của Trái Đất, bán kính 9 000 km. Biết rằng vệ tinh chuyển động hết một vòng của quỹ đạo trong 2 h. a) Hãy tính quãng đường vệ tinh đã chuyển động được sau: 1 h; 3 h; 5 h. b) Vệ tinh chuyển động được quãng đường 200 000 km sau bao nhiêu giờ (làm tròn kết quả đến hàng đơn vị)?

Phương pháp giải - Xem chi tiết

Công thức tính chu vi hình tròn là \(2.R.\pi \) với R là bán kính đường tròn.

Lời giải chi tiết

a) Vệ tinh chuyển động hết một vòng của quỹ đạo tức là vệ tinh chuyển động được quãng đường bằng chu vi của quỹ đạo là đường tròn với tâm là tâm O của Trái Đất, bán kính 9 000 km.Do đó quãng đường vệ tinh đã chuyển động được sau 2 h là:2π . 9 000 = 18 000π (km). Quãng đường vệ tinh đã chuyển động được sau 1 h là:

\(\frac{18000.\pi}{2}.1 = 9000.\pi\) (km).

Quãng đường vệ tinh đã chuyển động được sau 3 h là: 

\(\frac{18000.\pi}{2}.3 = 27000.\pi\) (km).

Quãng đường vệ tinh đã chuyển động được sau 5 h là: \(\frac{18000.\pi}{2}.5 = 45000.\pi\) (km).b) Ta thấy vệ tinh chuyển động được quãng đường là 9000π (km) trong 1h.Vậy vệ tinh chuyển động được quãng đường 200 000 km trong thời gian là:\(\frac{200000}{9000\pi} \approx 7 \)  (giờ).

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