Question

A ball is thrown from the roof with a speed of of 15m/s at an angle of 45° with the horizontal . At what distance will it hit the field again .​

Answer 1

Question

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• A ball is thrown from the roof with a speed of of 15 m/s at an angle of 45° with the horizontal. At what distance will it hit the field again?

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Answer

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• Distance at which the ball will hit the field again is 22.5 m.

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Step – By – Step Explanation

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Given

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• Velocity (u) = 15 m/s

• Angle with horizontal θ = 45°

• Acceleration due to gravity (g) = 10 m/s²

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To Find

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• Horizontal range (R)?

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Solution

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• Here, we know velocity, angle with horizontal and acceleration due to gravity and we have to find distance at which it will hit the field again i.e, we have to find horizontal range, we know that it is given by :

• $\bigstar\:\pmb{\underline{\boxed{\bf{\red{R = \dfrac{u^2sin2\theta}{g}}}}}}$

• Where, R denotes horizontal range, u denotes velocity, θ denotes angle with horizontal and g denotes acceleration due to gravity.

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★ Putting all values in formula :

$\\ :\implies\:\sf R = \dfrac{\big(15\big)^2\:\times\:sin\big(2\:\times\:45\big)}{10}$

$\\ :\implies\:\sf R = \dfrac{225\:\times\:sin90^{\circ}}{10}$

$\\ :\implies\:\sf R = \dfrac{225\:\times\:1}{10}$

$\\ :\implies\:\sf R = {\cancel{\dfrac{225}{10}}}$

$\\ :\implies\:\pmb{\blue{\underline{\boxed{\bf{\pink{R = 22.5}}}}}}$

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• Therefore, distance at which the ball will hit the field again is 22.5 m.

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Answer 2

Answer:

22.5m is the required answer .

Explanation:

According to the Question

It is given that ball is thrown from the roof with a speed of of 15m/s at an angle of 45° with the horizontal .

we need to calculate the distance will it hit the field again.

As we know that acceleration due to gravity is 10m/s².

Using horizontal range formula

Let the distance will it hit the field be d metres .

• horizontal range = u²sin2∅/g

where,

u denote velocity

g denote acceleration due to gravity

Substitute the value we get

➻ horizontal range = 15²Sin(2×45)/10

➻ horizontal range = 225×Sin90°/10

➻ horizontal range = 225×1/10

➻ horizontal range = 225/10

➻ horizontal range = 22.5m

• Hence, the ball hits the roof again 22.5 metres from the point of projection .