An object is thrown horizontally from a height of 45 m. How long will it take to

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Question: An object is thrown horizontally from a height of 45 m. How long will it take to hit the ground? (Take g = 10 m/s²) (2022)

Options:

Correct Answer: 4 s

Exam Year: 2022

Solution:

Using h = (1/2)gt², 45 = (1/2)(10)t². Solving gives t² = 9, so t = 3 s.

An object is thrown horizontally from a height of 45 m. How long will it take to hit the ground? (Take g = 10 m/s²) (2022)

An object is thrown horizontally from a height of 45 m. How long will it take to hit the ground? (Take g = 10 m/s²) (2022)

Step 1: Identify the height from which the object is thrown. In this case, the height (h) is 45 meters.
Step 2: Use the formula for the distance fallen under gravity, which is h = (1/2)gt², where g is the acceleration due to gravity (10 m/s²).
Step 3: Substitute the values into the formula: 45 = (1/2)(10)t².
Step 4: Simplify the equation: 45 = 5t² (since (1/2)(10) = 5).
Step 5: To isolate t², divide both sides by 5: t² = 45 / 5.
Step 6: Calculate 45 / 5, which equals 9. So, t² = 9.
Step 7: To find t, take the square root of both sides: t = √9.
Step 8: Calculate the square root of 9, which is 3. Therefore, t = 3 seconds.

Projectile Motion – The question tests understanding of the time of flight for an object in free fall, independent of horizontal motion.
Kinematic Equations – Application of the kinematic equation for vertical motion to determine the time taken to fall a certain height.