1. Answer:

Given:

Height of the mountain (h) = 150 m

Horizontal distance fallen (d) = 30 m

Acceleration due to gravity (g) = 9.8 m/s^2

Calculating time taken to fall vertically (t):

We can use the equation of motion for vertical motion:

h = (1/2) * g * t^2

Plugging in the values, we get:

150 = (1/2) * 9.8 * t^2

Solving for t, we get:

t^2 = (2 * 150) / 9.8

t^2 ≈ 30.6122449

t ≈ 5.53 seconds (rounded to two decimal places)

Calculating initial horizontal velocity (v_x):

We can use the equation for horizontal distance:

d = v_x * t

Plugging in the values, we get:

30 = v_x * 5.53

Solving for v_x, we get:

v_x ≈ 5.42 m/s (rounded to two decimal places)

Calculating initial vertical velocity (v_y):

We can use the equation of motion for vertical motion:

v_y = g * t

Plugging in the values, we get:

v_y ≈ 9.8 * 5.53

v_y ≈ 54.39 m/s (rounded to two decimal places)

So, the correct solution is:

Time taken to fall vertically (t) ≈ 5.53 seconds

Initial horizontal velocity (v_x) ≈ 5.42 m/s

Initial vertical velocity (v_y) ≈ 54.39 m/s