A stone is thrown horizontally from the top of a cliff 80 m high. How far from t

A stone is thrown horizontally from the top of a cliff 80 m high. How far from the base of the cliff will it land?

A stone is thrown horizontally from the top of a cliff 80 m high. How far from the base of the cliff will it land?

Correct Answer: 40.4 m

Step 1: Identify the height of the cliff, which is 80 meters.
Step 2: Use the formula to calculate the time it takes for the stone to fall: Time = √(2h/g), where h is the height (80 m) and g is the acceleration due to gravity (approximately 9.8 m/s²).
Step 3: Plug in the values: Time = √(2 * 80 / 9.8).
Step 4: Calculate the value inside the square root: 2 * 80 = 160, then 160 / 9.8 ≈ 16.33.
Step 5: Take the square root of 16.33 to find the time: Time ≈ √16.33 ≈ 4.04 seconds.
Step 6: Determine the horizontal speed of the stone. In this case, it is assumed to be 10 m/s.
Step 7: Use the formula for horizontal distance: Distance = horizontal speed * time.
Step 8: Plug in the values: Distance = 10 m/s * 4.04 s.
Step 9: Calculate the distance: 10 * 4.04 = 40.4 meters.
Step 10: Conclude that the stone will land approximately 40.4 meters from the base of the cliff.

Projectile Motion – The question tests understanding of projectile motion, specifically the horizontal and vertical components of motion.
Free Fall – It assesses the ability to calculate the time of free fall from a height using the formula derived from gravitational acceleration.
Horizontal Motion – It evaluates the understanding of how horizontal motion is independent of vertical motion in projectile motion.