Question

A cricket ball is thrown at a speed of 28m/s at an angle 30 from the horizontal. The ratio of range to height is

Answer 1

Explanation:

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Answer 2

Solution :

⏭ Given:

✏ Velocity of projection = 28mps

✏ Angle of projection = 30°

⏭ To Find:

✏ Ratio of range to height

⏭ Formula:

• Range

$\star \: \underline{ \boxed{ \bold{ \sf{ \pink{R = \dfrac{ {u}^{2} \sin2 \theta }{g}}}}}} \: \star$

• Maximum Height

$\star \: \underline{ \boxed{ \bold{ \sf{ \blue{H = \dfrac{ {u}^{2} { \sin}^{2} \theta }{2g}}}}}} \: \star$

⏭ Calculation:

$\mapsto \sf \: \red{ \dfrac{Range}{Height} = \dfrac{ 2\sin2 \theta}{ { \sin}^{2} \theta } } \\ \\ \mapsto \sf \: \dfrac{R}{H} = \dfrac{2 \sin60 \degree}{ { \sin}^{2} 30 \degree} \\ \\ \mapsto \sf \: \dfrac{R}{H} = 2 \times \dfrac{ \sqrt{3} }{2} \times 4 \\ \\ \gray{ \bigstar} \: \underline{ \boxed{ \bold{ \sf{ \orange{ \large{R : H = 4 \sqrt{3} }}}}}} \: \gray{ \bigstar}$

⏭ Additional information:

• A body is said to be projectile if is projected into space with some initial velocity and then it continuous to move in a vertical planr such that its horizontal acceleration is zero and verticle downward acceleration is equal to g.
• In projectile motion, the horizontal motion and the vertical motion are independent of each other.