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. group of answer choices

O 58 m
O 197 m
O 154 m
O 120 m

Answer 1

The stone thrown from the cliff with an initial velocity of 12 m/s at a 30-degree angle travels approximately 58 meters horizontally before reaching the bottom, based on the constant horizontal component of velocity and the time of flight.

Step-by-step explanation:

We need to find out how far horizontally a stone travels if it is thrown with an initial speed of 12 m/s at a 30° angle above the horizontal and takes 5.6 seconds to reach the bottom of the cliff. Neglecting air resistance, this can be viewed as a problem involving projectile motion.

Firstly, the horizontal velocity component (Vx) is not affected by gravity and will remain constant throughout the motion. We can calculate Vx using the initial speed and the cosine of the angle:

• Vx = V0 cos(θ) = 12 m/s cos(30°) = 12 m/s * (√3/2) = 10.392 m/s (approximately)

The horizontal distance traveled (Dx) is simply the horizontal velocity multiplied by the time in the air:

• Dx = Vx * t = 10.392 m/s * 5.6 s = 58.1952 m

Therefore, the stone travels approximately 58 meters horizontally before reaching the bottom of the cliff.