COMEDK · Physics · 4. Motion In Two Dimensions

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 is ( \(g\) is 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 \(\frac{g t_{1} t_{2}}{t_{1}+t_{2}}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{g\left(t_{1}+t_{2}\right)}{2}\)

Step-by-step Solution

Detailed explanation

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

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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