Question

A stone is projected from a point on the ground
with a velocity of 98 ms -1 at an elevaton of 30°
Find the greatest height attained, (ii) the time
of flight and (m) the honzontal range of the
projectile​

Answer 1

Given :

• Initial velocity of the projectile = 98 m/s
• Elevation = 30°

To Find :

• The maximum attained , time of flight and the horizontal range

Solution :

Maximum height attained by the projectile is given by ,

$\\ \star \: {\boxed{\sf{\purple{H_{max}= \frac{ {u}^{2} {sin}^{2} \theta}{2g} }}}}$

$\\ \sf{where} \begin{cases}& \sf{u \: is \: initial \: velocity} \\ & \sf{ \theta \: is \: angle \: of \: projection} \\ &\sf{g \: is \: acceleration \: due \: to \: gravity} \end{cases}$

Substituting the values we have ,

$\\ : \implies \sf \: H_{max} = \frac{ {(98)}^{2} {sin}^{2} (30 {}^{ \circ}) }{2(9.8)}$

$\\ : \implies \sf \: H_{max} = \frac{98 \times 98 \times { \big( \frac{1}{2} } \big) {}^{2} }{9.8 \times 2}$

$\\ : \implies \sf \: H_{max} = \frac{98 \times 98 \times 1}{4 \times 19.6}$

$\\ : \implies\underline{\boxed{\sf{\pink{H_{max} = 122.5 \: m}}}} \: \bigstar$

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The time of flight of a projectile is given by,

$\\ \star \: {\boxed{\purple{\sf{t_f = \frac{2usin\theta}{g} }}}}$

Substituting the values we have ,

$\\ : \implies \sf \: t_f = \frac{2(98)sin30^{\circ}}{(9.8)}$

$\\ : \implies \sf \: t_f = \frac{196\times \frac{1}{2}}{9.8}$

$\\ : \implies{\underline{\boxed{\pink{\sf{t_f = 10 \: sec}}}}} \: \bigstar$

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Range of a projectile is given by ,

$\\ \star \: {\boxed{\purple{\sf{R = \frac{ {u}^{2} \sin2 \theta }{g} }}}}$

Substituting the values we have ,

$\\ : \implies \sf \: R= \frac{(98) {}^{2} \times \sin(2 \times 30 {}^{ \circ} ) }{9.8}$

$\\ : \implies \sf \: R = \frac{9604 \times \sin( {60}^{ \circ} ) }{9.8}$

$\\ : \implies \sf \: R = \frac{9604 \times \frac{ \sqrt{3} }{2} }{9.8}$

$\\ : \implies \sf \: R= \frac{9604 \times \sqrt{3} }{9.8 \times 2}$

$\\ : \implies{\underline{\boxed{\pink{\sf{R= 848.7 \:m }}}}} \: \bigstar$

Hence ,

• The Maximum height , Range and Time of flight of the given projectile are 122.5 m , 10 sec and 848.7 m