An object is dropped from the top of a tower. If it takes 4s for it to reach the ground, calculate the height…

Analyze the question An object is dropped (so initial velocity u = 0) and falls freely for t = 4 s. We need the height h of the tower.

Concept For free fall from rest, use the equation of motion:

h = ut + ½gt²

Since u = 0, this simplifies to:

h = ½gt²

Solution

• u = 0 m/s
• g = 10 m/s²
• t = 4 s

h = ½ × 10 × (4)² h = ½ × 10 × 16 h = 5 × 16 h = 80 m

Answer: C. 80 m

Tip: For objects dropped from rest with g = 10, memorize the pattern h = 5t². At 1 s, 5 m; at 2 s, 20 m; at 3 s, 45 m; at 4 s, 80 m. A common mistake is to forget to square the time. Using h = 5 × 4 = 20 m (option A) is a trap, and doubling 80 to 160 comes from forgetting the ½.