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 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 \((g=10\,\text{m s}^{-2})\):
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At maximum height, the vertical component of velocity becomes zero. Use only the vertical component of velocity for calculating maximum height.
Updated On: Jun 26, 2026
- \(8.75 \, \text{m}\)
- \(5.50 \, \text{m}\)
- \(6.25 \, \text{m}\)
- \(10 \, \text{m}\)
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The Correct Option is C
Solution and Explanation
Step 1: Identify the vertical component of velocity.
At height \(5 \, \text{m}\), velocity is \[ \vec{V}=5\hat{i}+5\hat{j} \] So, vertical velocity at this height is \[ v_y=5\,\text{m s}^{-1} \]
Step 2: Use vertical motion equation.
From height \(5 \, \text{m}\) to maximum height, final vertical velocity becomes zero.
So, \[ v^2=u^2+2as \] Here, \[ v=0,\quad u=5,\quad a=-10 \] Therefore, \[ 0^2=5^2+2(-10)s \] \[ 0=25-20s \] \[ 20s=25 \] \[ s=1.25\,\text{m} \]
Step 3: Find maximum height from ground.
The ball is already at height \[ 5\,\text{m} \] Additional height gained is \[ 1.25\,\text{m} \] Thus, maximum height is \[ H=5+1.25=6.25\,\text{m} \]
Step 4: Final conclusion.
Therefore, \[ \boxed{6.25\,\text{m}} \]
At height \(5 \, \text{m}\), velocity is \[ \vec{V}=5\hat{i}+5\hat{j} \] So, vertical velocity at this height is \[ v_y=5\,\text{m s}^{-1} \]
Step 2: Use vertical motion equation.
From height \(5 \, \text{m}\) to maximum height, final vertical velocity becomes zero.
So, \[ v^2=u^2+2as \] Here, \[ v=0,\quad u=5,\quad a=-10 \] Therefore, \[ 0^2=5^2+2(-10)s \] \[ 0=25-20s \] \[ 20s=25 \] \[ s=1.25\,\text{m} \]
Step 3: Find maximum height from ground.
The ball is already at height \[ 5\,\text{m} \] Additional height gained is \[ 1.25\,\text{m} \] Thus, maximum height is \[ H=5+1.25=6.25\,\text{m} \]
Step 4: Final conclusion.
Therefore, \[ \boxed{6.25\,\text{m}} \]
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