Physics Numerical Problems No. 3.11, Unit-3: Motion and Forces HSSC-I (class 11) Physics (Punjab Curriculum Textbook Board, Lahore) With Verified Answers

A ball is thrown horizontal from a height of 10 m with velocity of 21 m s⁻¹. How far off will it hit the ground and with what velocity?

(Ans: 30 m, 25 m s⁻¹)

Given:

Along X-Axis

Initial velocity =

v_{i x}

$\v_{ix}$ = 21 m s⁻¹

Acceleration =

a_{x}

$\a_x$ = 0 m s⁻²

Final velocity =

v_{f x}

$\v_{fx}$ = 21 m s⁻¹

Along Y-Axis

Initial velocity =

v_{i y}

$\v_{iy}$ = 0 m s⁻¹

Acceleration =

a_{y}

$\a_y$ = g = 9.8 m s⁻²

Height = y = h = 10 m

To Find:

Horizontal distance = x = ?

Final velocity =

v_{f}

$\v_f$ = ?

Solution:

We need find the time t first so using 2nd equation of motion along y-axis

y =

v_{i y}

$\v_{iy}$ t +

\frac{1}{2}

$\frac {1}{2}$ g t²

by putting the corresponding values

10 m = 0 m s⁻¹ ｘ t +

\frac{1}{2}

$\frac {1}{2}$ ｘ 9.8 m s⁻² ｘ t²

10 m = 0 + 4.9 m s⁻² ｘ t²

t² =

\frac{10 m}{4.9 m s ⁻ ²}

$\frac {10 m}{4.9 m s⁻²}$

t² =

\sqrt{\frac{100 m}{49 m s ⁻ ²}}

$\sqrt frac {100 m}{49 m s⁻²}$

t =

\frac{10}{7}

$\frac {10}{7}$ s -------------(1)

Now we know that along x-axis

x =

v_{i x}

$\v_{ix}$ t

x = 21 m s⁻¹ ｘ

\frac{10}{7}

$\frac {10}{7}$ s

x = 30 m ---------------Ans. (1)

Now using 1st equation of motion for projectile along y-axis

v_{f y}

$\v_{fy}$ =

v_{i y}

$\v_{iy}$ +

a_{y}

$\a_y$ t

putting the corresponding values

v_{f y}

$\v_{fy}$ = 0 m s⁻¹ + 9.8 m s⁻² ｘ

\frac{10}{7}

$\frac {10}{7}$ s

v_{f y}

$\v_{fy}$ = 14 m s⁻¹ --------------- Ans. (2)

The final speed vf at the time when it strike the ground is given by formula.

v_{f}

$\v_f$ =

\sqrt{v_{f x}^{2} + v_{f y}^{2}}

$\sqrt {v_{fx}^2 + v_{fy}^2}$

by putting the corresponding value

v_{f}

$\v_f$ =

\sqrt{{(21 m s ⁻ ¹)}^{2} + {(14 m s ⁻ ¹)}^{2}}

$\sqrt {(21 m s⁻¹)^2 + (14 m s⁻¹)^2}$

v_{f}

$\v_f$ =

\sqrt{441 m ² s ⁻ ² + 196 m ² s ⁻ ²}

$\sqrt {441 m² s⁻² + 196 m² s⁻²}$

v_{f}

$\v_f$ =

\sqrt{637 m ² s ⁻ ²}

$\sqrt {637 m² s⁻²}$

v_{f}

$\v_f$ = 25.13 m s⁻¹ -------------------Ans. (2)

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