A ball is thrown vertically downwards with a velocity of 20 m/s from the top of a tower. It hits the ground af

Question

A ball is thrown vertically downwards with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with the velocity of 80 m/s. The height of the tower is: (assuming g = 10 m/s²)

Accepted Answer

1.  **Identify Given Values:**
    *   Initial velocity, $u = 20 	ext{ m/s}$ (directed downwards).
    *   Final velocity, $v = 80 	ext{ m/s}$ (directed downwards).
    *   Acceleration, $a = g = 10 	ext{ m/s}^2$ (directed downwards).
    *   Displacement, $s = h$ (height of the tower).

2.  **Select Kinematic Equation:**
    Use the equation relating velocities, acceleration, and displacement for uniformly accelerated motion :
    $$ v^2 = u^2 + 2as $$

3.  **Substitute and Solve:**
    $$ (80)^2 = (20)^2 + 2(10)h $$
    $$ 6400 = 400 + 20h $$
    $$ 20h = 6400 - 400 $$
    $$ 20h = 6000 $$
    $$ h = \frac{6000}{20} = 300 	ext{ m} $$

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