আনুভূমিকের সাথে ${45}^{\circ }$ কোণে নিক্ষিপ্ত একটি বস্তুর আনুভূমিক পাল্লা 100m । এর সর্বোচ্চ উচ্চতা-

The answer of 25.00m for the maximum height of an object thrown at an angle of 45 degrees with a horizontal range of 100m is correct based on the principles of projectile motion.

Here’s a breakdown of how this works:

    
• Projectile Motion Basics: When an object is projected at an angle, its motion can be analyzed in two components: horizontal and vertical.
    
• Range Formula: For projectile motion, the range \( R \) is calculated using the formula:         R = (v^2 * sin(2θ)) / g,         where \( v \) is the initial speed, \( θ \) is the angle of projection, and \( g \) is the acceleration due to gravity.
    
• Maximum Height Formula: The maximum height \( H \) can be calculated using the formula:         H = (v^2 * sin^2(θ)) / (2g).
    
• Angle of 45 Degrees: At 45 degrees, the sine value maximizes the range, and both sine and cosine of the angle are equal.

By using the given range of 100m and applying the formulas, you find that the maximum height the object reaches is indeed 25.00m.

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