COMEDK · Physics · 3. Motion In One Dimension

A body is projected vertically upwards. The times corresponding to height \(h\) while ascending and while descending are \(t_1\) and \(t_2\), respectively. Then, the velocity of projection will be (take, \(g\) as acceleration due to gravity)

A \(\frac{g \sqrt{t_1 t_2}}{2}\)
B \(\frac{g\left(t_1+t_2\right)}{2}\)
C \(g \sqrt{t_1 t_2}\)
D \(g \frac{t_1 t_2}{\left(t_1+t_2\right)}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{g\left(t_1+t_2\right)}{2}\)

Step-by-step Solution

Detailed explanation

Let \(v\) be initial velocity of vertical projection and \(t\) be the time taken by the body to reach a height \(h\) from ground. Here, \(\quad u=u, a=-g, s=h, t=t\) Using, \(s=u t+\frac{1}{2} a t^2\), we have…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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