Question 18
A ball thrown up vertically returns to the thrower after 6 s. Find
(a) the velocity with which it was thrown up,
(b) the maximum height it reaches, and
(c) its position after 4s.
Given,
Ball returns to thrower in 6s. So, timeup + timedown = 6 s hence, timeup = 3 s.
g = 9.8 ms-2
(a) Final velocity (v) = 0
From first equation of motion
v = u – gtup
⇒ u = v + gtup
⇒ u = 0 + (9.8 x 3)
⇒ u = 29.4 ms-1
Hence, the velocity with which it was thrown up = 29.4 ms-1.
(b) According to the second equation of motion,
S = ut - gt2
Substituting we get,
S = (29.4 x 3) - ( x 9.8 x 3 x 3)
= 88.2 - 44.1 = 44.1 m
Hence, maximum height stone reaches is 44.1 m
(c) In 3 sec, it reaches the maximum height.
Distance travelled in another 1 sec = s'
According to the second equation of motion,
S = ut + gt2
g is +ve as ball is going down
Substituting we get,
S = 0 + ( x 9.8 x 1 x 1)
= 4.9 m
Hence, in 4 sec the ball will be 4.9 m from the top or 39.2 m (i.e., 44.1 - 4.9) from the bottom.
Chapter 9: Gravitation — Quick Reference
Quick Revision Points
- F = Gm₁m₂/r² (G = 6.674 × 10⁻¹¹ N·m²/kg²)
- g = GM/R² = 9.8 m/s² (Earth); g on Moon ≈ g/6
- Mass (kg, constant) vs Weight (N = mg, varies with location)
- Pressure P = F/A (Pa = N/m²); Fluid pressure P = hρg
- Archimedes: buoyant force = weight of displaced fluid
- Float if density < fluid density; Sink if density > fluid density
- Relative density = density of substance / density of water (no unit)
- Read the detailed chapter notes for complete coverage of all NCERT topics.
- Practice all NCERT in-text and back exercise questions — they are frequently asked in exams.
- Focus on comparison tables, diagrams, and definitions — these are high-scoring areas.
- For numericals (if applicable), practice at least 20 problems of varying difficulty.
- Refer to the practice question bank (200+ questions) for thorough preparation.
- Detailed Notes: ch09-gravitation.html
- Practice Questions: 100+ questions with answers in 05-practice-questions/
- Chapter Test: 30-mark test paper in 06-tests/chapter-tests-30marks/
- Formula Sheet: Complete formula reference in 03-teacher-aid/formula-sheet.html