A man runs for an hour and a half at 8 miles an hour due south. He then continues south on a bus traveling at 55 miles an hour f
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Answer:
a) v₀ = 69.29 m / s , b) t = 18.84 s
Explanation:
a) For this exercise we will use the projectile launch equations
x = v₀ₓ t
y = y₀ + t - ½ g t²
Let's fix our reference system on the volcano, so the horizontal distance x = 1 km = 1000 m and the vertical distance y = -900 m, the initial height of the crater is I = 0 m. Let's replace to find the speeds
v_{oy} = v₀ sin θ
v₀ₓ = v₀ cos θ
y = v₀ sin θ (x / v₀ cos θ) - ½ g (x / v₀ cos θ)2
y = x tan θ - ½ g x² / v₀² sec² θ
½ g x² sec² θ / v₀² = x tan θ - y
v₀² = ½ g x² sec² θ / (x tan θ –y)
Let's calculate
v₀² = ½ 9.8 1000² sec² 40 / (1000 tan 40 - (-900))
v₀ = √ (8.35 10⁶ / 1,739 10³)
v₀ = 69.29 m / s
b) Flight time
x = v₀ₓ t
t = x / v₀ cos θ
t = 1000 / 69.29 cos 40
t = 18.84 s