Question:
A ball rolls off the top of stairway with a horizontal velocity of magnitude $1.8~m/s$. The steps are 0.20 m high and 0.20 m wide. Which step will the ball hit first?
A ball rolls off the top of stairway with a horizontal velocity of magnitude $1.8~m/s$. The steps are 0.20 m high and 0.20 m wide. Which step will the ball hit first?
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A ball rolls off the top of stairway with a horizontal velocity of magnitude $1.8~m/s$. The steps are 0.20 m high and 0.20 m wide. Which step will the ball hit first?
Updated On: Apr 15, 2026
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- Second
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- Fourth
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The Correct Option is D
Solution and Explanation
Step 1: Equations
Vertical: $ny = \frac{1}{2}gt^{2}$. Horizontal: $nx = ut \Rightarrow t = \frac{nx}{u}$.
Step 2: Substitution
$ny = \frac{1}{2}g \times \frac{n^{2}x^{2}}{u^{2}} \Rightarrow n = \frac{2u^{2}y}{gx^{2}}$.
Step 3: Calculation
$n = \frac{2 \times (1.8)^{2} \times 0.20}{9.8 \times (0.20)^{2}} \approx 3.3$. The ball hits the 4th step.
Final Answer: (D)
Vertical: $ny = \frac{1}{2}gt^{2}$. Horizontal: $nx = ut \Rightarrow t = \frac{nx}{u}$.
Step 2: Substitution
$ny = \frac{1}{2}g \times \frac{n^{2}x^{2}}{u^{2}} \Rightarrow n = \frac{2u^{2}y}{gx^{2}}$.
Step 3: Calculation
$n = \frac{2 \times (1.8)^{2} \times 0.20}{9.8 \times (0.20)^{2}} \approx 3.3$. The ball hits the 4th step.
Final Answer: (D)
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