Question

a stone is thrown with an initial speed of 12 m/s at an angle of 30o above the horizontal from the top edge of a cliff. if it takes the stone 5.6 s to reach the bottom, how far does the stone travel horizontally? neglect air resistance.

Answer 1

To find the horizontal distance a stone travels when thrown from a cliff, use the initial speed and angle to calculate horizontal velocity, then multiply by time. The stone in question travels approximately 58.18 meters horizontally.

Step-by-step explanation:

To determine how far the stone travels horizontally when thrown from a cliff with an initial speed of 12 m/s at a 30° angle above the horizontal until it hits the bottom after 5.6 seconds, we use the concepts of projectile motion.

First, we find the horizontal velocity component (v_x) using the initial speed (v_0) and the cosine of the angle:

v_x = v_0 \times cos(\theta)

For our case,

v_x = 12 m/s \times cos(30°) = 12 m/s \times (\sqrt{3}/2) ≈ 10.39 m/s.

Now, since there is no horizontal acceleration (assuming negligible air resistance), the horizontal velocity remains constant. We can calculate the horizontal distance traveled as:

Horizontal Distance = v_x \times time

For our case,

Horizontal Distance = 10.39 m/s \times 5.6 s ≈ 58.18 meters.

Therefore, the stone travels approximately 58.18 meters horizontally before reaching the bottom of the cliff.