Question

a ball rolls offf the top of a step ladder with a horizontal velocity of 10m/s if the steps are 1m high and 1m wide the ball will just hit a03rd step b)20th step c)12th step d) 10th step

Answer 1

a ball rolls off the top of a step ladder with a horizontal velocity of $10\mathrm{m / s}$ if the steps are 1m high and 1m wide the ball will just hit a)03rd step b)20th step c)12th step d) 10th step

Solution

$\mathrm{V} = 10\frac{\mathrm{m}}{\mathrm{s}}$ -horizontal velocity of the ball;

$\mathrm{h} = 1\mathrm{m}$ -high of one step;

$\mathrm{d} - 1\mathrm{m}$ -width of one step;

The equation of motion for the ball along the X-axis (N-number of steps that the ball flew, t - time of the flight):

x: $\mathrm{N} \cdot \mathrm{d} = \mathrm{{Vt}}$

$$t = \frac {N d}{V}$$

The equation of motion for the ball along the Y-axis

y: $\mathrm{N} \cdot \mathrm{h} = \frac{\mathrm{gt}^2}{2}$ (2)

(1)in(2):

$$\mathrm {N h} = \frac {\mathrm {g}}{2} \cdot \frac {\mathrm {N} ^ {2} \mathrm {d} ^ {2}}{\mathrm {V} ^ {2}}$$ $$2 \mathrm {h V} ^ {2} = \mathrm {g N d} ^ {2}$$ $$N = \frac {2 h V ^ {2}}{g d ^ {2}} = \frac {2 \cdot 1 m \cdot (1 0 \frac {m}{s}) ^ {2}}{9 . 8 \frac {m}{s ^ {2}} \cdot (1 m) ^ {2}} = 2 0. 4 \approx 2 0 \text {s t e p s}$$

Answer: b) 20th step.