Answer:
Lauch velocity (u) = 26.15 m/s
Lauch Angle (θ) = 35°
Explanation:
From the question given above, the following data were obtained:
Range (R) = 65 m
Time of flight (T) = 3 s
Acceleration due to gravity (g) = 10 m/s²
Lauch velocity (u) =?
Lauch Angle (θ) =?
R = u²Sin2θ /g
65 = u² × Sin2θ /10
Recall:
Sin2θ = 2SinθCosθ
65 = u² × 2SinθCosθ / 10
65 = u² × SinθCosθ / 5
Cross multiply
65 × 5 = u² × SinθCosθ
325 = u² × SinθCosθ .....(1)
T = 2uSinθ / g
3 = 2uSinθ / 10
3 = uSinθ / 5
Cross multiply
3 × 5 = uSinθ
15 = u × Sinθ
Divide both side by Sinθ
u = 15 / Sinθ....... (2)
Substitute the value of u in equation (2) into equation (1)
325 = u² × SinθCosθ
u = 15 / Sinθ
325 = (15 / Sinθ)² × SinθCosθ
325 = 225 / Sin²θ × SinθCosθ
325 = 225 × SinθCosθ / Sin²θ
325 = 225 × Cosθ / Sinθ
Cross multiply
325 × Sineθ = 225 × Cosθ
Divide both side by Cosθ
325 × Sineθ / Cosθ = 225
Divide both side by 325
Sineθ / Cosθ = 225 / 325
Sineθ / Cosθ = 0.6923
Recall:
Sineθ / Cosθ = Tanθ
Tanθ = 0.6923
Take the inverse of Tan
θ = Tan¯¹ 0.6923
θ = 35°
Substitute the value of θ into equation (2) to obtain the value of u.
u = 15 / Sinθ
θ = 35°
u = 15 / Sin 35
u = 15 / 0.5736
u = 26.15 m/s
Summary:
Lauch velocity (u) = 26.15 m/s
Lauch Angle (θ) = 35°
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Answer:
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