Answer:
The initial velocity of the golf is 15.7 m/s.
The direction of the golf is 57°.
Step-by-step explanation:
The following data were obtained from the question:
Time of flight (T) = 2.7 secs
Range (R) = 23 m
Acceleration due to gravity (g) = 9.8 m/s²
Initial velocity (u) =.?
Direction (θ) =.?
T = 2U Sine θ /g
2.7 = 2 × U × Sine θ /9.8
Cross multiply
2.7 × 9.8 = 2 × U × Sine θ
26.46 = 2 × U × Sine θ
Divide both side by 2 × Sine θ
U = 26.46 /2 Sine θ
U = 13.23 / Sine θ ... (1)
R = U² Sine 2θ /g
23 = U² Sine 2θ / 9.8
U = 13.23 / Sine θ
23 = (13.23/ Sine θ)² Sine 2θ / 9.8
23 = (175.0329 / Sine² θ) × Sine 2θ / 9.8
23 = 17.8605/Sine² θ × Sine 2θ
Recall:
Sine 2θ = 2SineθCosθ
23 = 17.8605/ Sine² θ × 2SineθCosθ
23 = 17.8605/ Sine θ × 2Cosθ
23 = 35.721 Cos θ /Sine θ
Cross multiply
23 × Sine θ = 35.721 Cos θ
Divide both side by 23
Sine θ = 35.721 Cos θ /23
Sine θ = 1.5531 × Cos θ
Divide both side by Cos θ
Sine θ /Cos θ = 1.5531
Recall:
Sine θ /Cos θ = Tan θ
Sine θ /Cos θ = 1.5531
Tan θ = 1.5531
Take the inverse of Tan
θ = Tan¯¹ (1.5531)
θ = 57°
Therefore, the direction of the golf is 57°
Thus, the initial velocity can be obtained as follow:
U = 13.23 / Sine θ
θ = 57°
U = 13.23 / Sine 57
U = 13.23/0.8387
U = 15.7 m/s
Therefore, the initial velocity of the golf is 15.7 m/s