A ball is thrown vertically upward with a speed of $20$ m/s from the top of a tower $25$ m high and finally lands at the foot of the tower. Take $g = 10\ \text{m/s}^2$ and neglect air resistance.
A. The maximum height of the ball above the ground is $45$ m.
B. The ball reaches the ground $5$ s after it is thrown.
C. The average speed of the ball over the whole flight is $13$ m/s.
D. The magnitude of the average velocity of the ball over the whole flight is $9$ m/s.
Choose the correct answer from the options given below:
Answer: (D) A, B and C only
Concept. Take upward as positive with the origin at the top of the tower. Average speed uses the total path length; average velocity uses the net displacement.
Step 1. Maximum height. Rise above the tower: $\dfrac{u^2}{2g} = \dfrac{400}{20} = 20$ m, so $25 + 20 = 45$ m above the ground. A is correct.
Step 2. Time of flight. Displacement $-25$ m:
$$-25 = 20t - 5t^2 \;\Rightarrow\; t^2 - 4t - 5 = 0 \;\Rightarrow\; t = 5\ \text{s}$$
B is correct.
Step 3. Average speed. Path $= 20$ m up $+ 45$ m down $= 65$ m:
$$\frac{65}{5} = 13\ \text{m/s}$$
C is correct.
Step 4. Average velocity. Net displacement $25$ m downward:
$$\frac{25}{5} = 5\ \text{m/s}$$
not $9$ m/s, so D is wrong.
Answer. A, B and C only (Option D).
Solution by Sreeraj P, M.Sc Physics