Question

A ball is projected from ground into the air. At the height of \(5 \, \text{m}\), its velocity is \(\vec{V}=(5\hat{i}+5\hat{j})\,\text{m s}^{-1}\). The maximum height reached by the ball is \((g=10\,\text{m s}^{-2})\):

• A. \(8.75 \, \text{m}\)
• B. \(5.50 \, \text{m}\)
• C. \(6.25 \, \text{m}\)
• D. \(10 \, \text{m}\)

Hint:

At maximum height, the vertical component of velocity becomes zero. Use only the vertical component of velocity for calculating maximum height.

Answer 1

The Correct Option is C

Step 1: Isolate the vertical component at h = 5 m.
Velocity at 5 m: \( \vec{V} = 5\hat{i}+5\hat{j} \) m/s. Vertical component \( v_y = 5 \) m/s.

Step 2: Use energy conservation for the remaining rise.
\[ \Delta h = \frac{v_y^2}{2g} = \frac{25}{2\times10} = 1.25\,\text{m} \] Maximum height \( = 5 + 1.25 \) \[ \boxed{6.25\,\text{m}} \]