A soccer player kicks a ball so that the ball leaves the ground at an angle of 35- above the horizontal and lands on the ground 25 meters away- Determine the speed at which the ball left the ground- in m-s

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Byju's Answer

Standard X

Mathematics

Calculating Heights and Distances

A soccer play...

Question

A soccer player kicks a ball so that the ball leaves the ground at an angle of $35^{\circ}$ above the horizontal and lands on the ground $25$ meters away. Determine the speed at which the ball left the ground. (in m/s)

16.14

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20.7

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Solution

The correct option is A $16.14$
In this problem we have motion of projectile, It starts at the ground level and ends at the ground level.
Distance traveled in horizontal direction in terms of initial speed and launch angle
$d = \frac{v_{1}^{2} sin 2 θ}{g}$
distance $= d = 25 m$
launch angle $θ = 35 °$
free fall acceleration $= g$
$g = 9.8 ㎨$
$∴ 25 = \frac{v_{1}^{2} sin 70 °}{9.8}$ ... (by substituting values)
$∴ v_{1} = \sqrt{\frac{25 \times 9.8}{sin 70 °}}$
$= 16.15 ㎧$

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A soccer player kicks a ball so that the ball leaves the ground at an angle of 35∘ above the horizontal and lands on the ground 25 meters away. Determine the speed at which the ball left the ground. (in m/s)

A soccer player kicks a ball so that the ball leaves the ground at an angle of $35^{\circ}$ above the horizontal and lands on the ground $25$ meters away. Determine the speed at which the ball left the ground. (in m/s)