A stone is dropped from a height of 45 m. How far will it travel horizontally if

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Question: A stone is dropped from a height of 45 m. How far will it travel horizontally if it is projected horizontally with a speed of 10 m/s?

Options:

Correct Answer: 40 m

Solution:

Time to fall t = √(2h/g) = √(90/9.8) ≈ 4.27 s; horizontal distance = 10 * 4.27 ≈ 42.7 m.

A stone is dropped from a height of 45 m. How far will it travel horizontally if it is projected horizontally with a speed of 10 m/s?

A stone is dropped from a height of 45 m. How far will it travel horizontally if it is projected horizontally with a speed of 10 m/s?

Step 1: Identify the height from which the stone is dropped. In this case, it is 45 meters.
Step 2: Use the formula to calculate the time it takes for the stone to fall. The formula is t = √(2h/g), where h is the height (45 m) and g is the acceleration due to gravity (approximately 9.8 m/s²).
Step 3: Plug in the values into the formula: t = √(2 * 45 / 9.8).
Step 4: Calculate the value inside the square root: 2 * 45 = 90, so t = √(90 / 9.8).
Step 5: Calculate 90 / 9.8, which is approximately 9.18.
Step 6: Find the square root of 9.18, which is approximately 3.03 seconds. (Note: The short solution states 4.27 seconds, which seems to be an error in the height used.)
Step 7: Now, calculate the horizontal distance traveled. The stone is projected horizontally at a speed of 10 m/s.
Step 8: Use the formula for horizontal distance: distance = speed * time. Here, distance = 10 m/s * 3.03 s.
Step 9: Calculate the horizontal distance: 10 * 3.03 = 30.3 meters.

Projectile Motion – The question tests understanding of the principles of projectile motion, specifically the separation of vertical and horizontal components of motion.
Free Fall – It assesses knowledge of free fall under gravity, including the calculation of time taken to fall from a certain height.