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2 years ago

If the range of a projectile is and 256√3 m in the maximum height reached is 64 m. calculate the angle of projection

Physics

1 answer:

yawa3891 [41]2 years ago

5 0

The angle of projection given that the range is 256√3 m and the maximum height reached is 64 m is 30°

<h3>Data obtained from the question</h3>

Range (R) = 256√3 m
Maximum height (H) = 64 m
Acceleration due to gravity (g) = 9.8 m/s²
Angle of projection (θ) = ?

<h3>How to determine the angle of projection</h3>

R = u²Sine(2θ) / g

256√3 = u²Sine(2θ) / 9.8

Cross multiply

256√3 × 9.8 = u²Sine(2θ)

Divide both sides by Sine(2θ)

u² = 256√3 × 9.8 / Sine(2θ)

H = u²Sine²θ / 2g

64 = [256√3 × 9.8 / Sine(2θ)] × [Sine²θ / 2 × 9.8]

64 = [256√3 / Sine(2θ)] × [Sine²θ / 2]

Recall

Sine²θ = SineθSineθ

Sine2θ = 2SineθCosθ

Thus,

64 = [256√3 / 2SineθCosθ] × [SineθSineθ / 2]

64 = 256√3 × Sineθ / 4Cosθ

Recall

Sineθ / Cosθ = Tanθ

Thus,

64 = 256√3 / 4 × Tanθ

Divide both side by 256√3 / 4

Tanθ = 64 ÷ 256√3 / 4

Tanθ = 0.5774

Take the inverse of Tan

θ = Tan⁻¹ 0.5774

θ = 30°

Learn more about projectile motion:

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Using formula of work done

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Put the value into the formula

$W=\int_{0}^{10}{27562.5\pi\\times(12-h)}dh$

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If the range of a projectile is and 256√3 m in the maximum height reached is 64 m. calculate the angle of projection​

If the range of a projectile is and 256√3 m in the maximum height reached is 64 m. calculate the angle of projection