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Bài 7.25 trang 50 SGK Toán 11 tập 2 - Cùng khám phá

Nếu một phi hành gia đứng trên Mặt Trắng và ném một viên đá từ độ cao 1 mét với vận tốc đầu 7,9 \(m/s\)
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Đề bài

Nếu một phi hành gia đứng trên Mặt Trắng và ném một viên đá từ độ cao 1 mét với vận tốc đầu 7,9 \(m/s\) thì chiếu cao của viên đá sau \(t\) giây được tính bởi công thức \(h\left( t \right) = 1 + 7,9t - 0,8{t^2}\) \(\left( m \right)\) (nguồn ). Tính vận tốc của viên đá khi chạm bề mặt Mặt Trăng. A. \( - 7,5m/s.\) B. \(8,1m/s.\) C. \(7,5m/s.\) D. \( - 8,1m/s.\)

Phương pháp giải - Xem chi tiết

Vận tốc \(v\left( t \right) = h'\left( t \right)\) Viên đá khi chạm đất thì \(h\left( t \right) = 0\). Giải phương trình tìm được thời gian viên đá chạm bề mặt Mặt Trăng Thay thời gian vừa tìm được vào vận tốc là tìm được vận tốc của viên đá khi chạm bề mặt Mặt Trăng

Lời giải chi tiết

Đáp án D

Ta có \(v\left( t \right) = h'\left( t \right) = 7,9 - 1,6t\)Viên đá khi chạm đất thì \(h\left( t \right) = 0\)\( \Leftrightarrow 1 + 7,9t - 0,8{t^2} = 0 \Leftrightarrow \left[ \begin{array}{l}t = 10\,\,\left( {TM} \right)\\t =  - \frac{1}{8}\,\,\left( {KTM} \right)\end{array} \right.\)Vậy vận tốc của viên đá khi chạm bề mặt Mặt Trăng là\(v\left( {10} \right) = 7,9 - 1,6.10 =  - 8,1\,\,m/s\)

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