A boy throws a ball into air at 45° from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is ___

A boy throws a ball into air at 45° from the horizontal to land it on a roof of a building of height H

Q. A boy throws a ball into air at 45° from the horizontal to land it on a roof of a building of height \(H\). If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of \(H\) is ____ m.

\((g = 10 \text{ m/s}^2)\)

(A) 20

(B) 25

(D) 15

Correct Answer: 15

Explanation

Time to reach maximum height is given as 2 s.

For vertical motion,

\[ t = \frac{u_y}{g} \]

So,

\[ u_y = g t = 10 \times 2 = 20 \text{ m/s} \]

Angle of projection is 45°, hence

\[ u_x = u_y = 20 \text{ m/s} \]

Vertical displacement after time \(t = 3\) s is given by

\[ y = u_y t - \frac{1}{2} g t^2 \]

Substitute values:

\[ y = 20 \times 3 - \frac{1}{2} \times 10 \times 3^2 \]

\[ y = 60 - 45 = 15 \]

Thus, the height of the building is

\[ H = \boxed{15 \text{ m}} \]

Hence, the correct answer is 15.

Explanation

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