A ball is thrown vertically upward with a velocity of 24.5 m s⁻¹. Find the greatest height it reaches and the time it takes to return to the thrower. (g = 9.8 m s⁻²)
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Write what is given. u = 24.5 m s⁻¹, v = 0 at the top, g = −9.8 m s⁻² for upward motion.
2 · Choose the equation for height. Use v² = u² + 2gs, since the time is not given.
3 · Find the height.
0 = (24.5)² + 2 × (−9.8) × s
19.6 s = 600.25
s = 600.25 ÷ 19.6 ≈ 30.6 m
4 · Find the time to the top. v = u + gt: 0 = 24.5 − 9.8 t, so t = 2.5 s.
5 · Find the total time. The time down equals the time up, so the total time = 2 × 2.5 = 5 s.
6 · Close. The ball rises about 30.6 m and returns to the thrower after 5 s.
Scoring tip: State the sign of g for upward motion before you substitute. Give a unit with every answer.
