At a particular instant, a hot air balloon is 100 m in the air and descending at a constant speed of 2.0 m/s. at this exact inst
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Answer:
x = 27.3 m
Explanation:
This is a projectile launching exercise, let's start by looking for the time it takes for the rock to reach the height of the window.
Let's use trigonometry to find the velocities of the rock
sin 40 = / v
cos 40 = v₀ₓ / v
v_{oy}= v sin 40
v₀ₓ = v cos 40
v_{oy} = 30 sin 40 = 19.28 m / s
v₀ₓ = v cos 40
v₀ₓ = 30 cos 40 = 22.98 m / s
we look for the time
= v_{oy}^2 - 2 g y
v_{y}^2 = 19.28 2 - 2 9.8 16 = 371.71 - 313.6 = 58.118
v_{y} = 7.623 m / s
we calculate the time
v_{y} = v_{oy} - gt
t = (v_{oy} - v_{y}) / g
t = (19.28 -7.623) / 9.8
t = 1,189 s
since the time is the same for both movements let's use this time to find the horizontal distance
x = v₀ₓ t
x = 22.98 1,189
x = 27.3 m