A hot air balloon is rising vertically at a constant speed of 5 m/s . An observer inside the balloon notes that the angle of depression of a fixed stone on the ground is 30^ . After 20 seconds, the observer notes that the angle of depression of the same stone has changed to 60^ . The horizontal distance of the stone from the point directly below the balloon on the ground is:

Step-by-step solution

Let the initial height of the balloon be h and the horizontal distance of the stone from the point directly below the balloon be d . From the initial observation, the angle of depression is 30^ . Thus, 30^ = h d h = d 3 The balloon rises at a constant speed of 5 m/s for 20 seconds. The vertical distance covered is: 5 20 = 100 m The new height of the balloon is h + 100 . The new angle of depression is 60^ . Thus, 60^ = h + 100 d h + 100 = d 3 Substituting the value of h from the first equation: d 3 + 100 = d 3 100 =