Question

A bouy lies 1000metres east and 2000m north of a start line. a boat starts at start line and travels on a bearing of 045deg at 6ms-1. After 6 mins the boat turnd and increases speed tp 9ms-1. How long does it tak boat to reach buoy?

Answer 1

Task:

A buoy lies 1000 m East and 2000 m North of a start line. A boat starts at start line and travels on a bearing of 45 deg at $6\frac{m}{s}$ . After 6 mins the boat turned and increased speed to $9\frac{m}{s}$ . How long does it take for the boat to reach buoy?

Solution:

$$s = v _ {0} t _ {1} + v _ {1} t _ {2}$$ $$v _ {0} = 6 \frac {m}{s}$$ $$t _ {1} = 1 2 0 \mathrm {s}$$ $$v _ {1} = 9 \frac {m}{s}$$ $$s _ {N o r t h} = v _ {0} (\sin 4 5 ^ {0}) t _ {1} + v _ {1} (\sin \propto) t _ {2}$$ $$s _ {E a s t} = v _ {0} (\cos 4 5 ^ {0}) t _ {1} + v _ {1} (\cos \propto) t _ {2}$$ $$s _ {N o r t h} = 2 0 0 0 m$$ $$s _ {E a s t} = 1 0 0 0 m$$

2000 m = 720 m (sin 45⁰) + 9 m/s (sin ∝)t₂

1000 m = 720 m (cos 45⁰) + 9 m/s (cos ∝)t₂

t₂ = 174.402 s

Answer:

t = t₁ + t₂ = 120 s + 174.402 s = 294.402 s