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Bài 1.6 trang 16 SGK Toán 11 tập 1 - Kết nối tri thức

Một người đi xe đạp với vận tốc không đổi, biết rằng bánh xe đạp quay được 11 vòng trong 5 giây.

♛Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

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

Một người đi xe đạp với vận tốc không đổi, biết rằng bánh xe đạp quay được 11 vòng trong 5 giây. a) Tính góc (theo độ và rađian) mà bánh xe quay được trong 1 giây. b) Tính độ dài quãng đường mà người đi xe đã đi được trong 1 phút, biết rằng đường kính của bánh xe đạp là 680 mm.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Tính số vòng quay được trong 1 giây, suy ra góc mà bánh xe quay được. Sử dụng công thức \(l = R\alpha \) để tính độ dài quãng đường.

Lời giải chi tiết

a) Trong 1 giây bánh xe quay được \(\frac{{11}}{5}\) vòng. Vì 1 vòng bằng \({360^0}\) nên góc mà bánh xe quay được trong 1 giây là:                  \(\frac{{11}}{5}{.360^0} = {792^0}\). Vì 1 vòng bằng \(2\pi \) nên góc mà bánh xe quay được trong 1 giây là:                  \(\frac{{11}}{5}.2\pi  = \frac{{22\pi }}{5}\;\left( {rad} \right)\). b) Ta có: 1 phút = 60 giây. Trong 60 giây, bánh xe quay được số vòng: \(\frac{{11}}{5}.60 = 132\) vòng. Chu vi bánh xe là \(C = 680\pi\) mm. Độ dài quãng đường người đó đi trong 1 phút là: \(680\pi. 132  =89760\pi\) mm.

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