two particles A and B are projected along different directions from the same point P on the ground with the same velocity of 70 M per second in the same vertical plane the hit the ground at the same point Q such that PQ is equals to 480m. Then:- [g=9.8m/s²]
(A)Ratio of their times of flight if 4:5
(B)Ratio of their maximum heights is 9:16
(C)Ratio of their minimum speeds during flights is 4:3
(D)The bisector of the angle between their directions of projection makes 45° with horizontal
Answers
Answer:
Step-by-step explanation:
Let say angle are α & β
Horizontal Speed = 70Cosα & 70Cosβ
Vertical Speed = 70Sinα & 70Sinβ
time to reach Peak Using V = U + aT
=> T = 70Sinα/g & 70Sinβ/g
Time of Flight = 2*70Sinα/g & 2*70Sinβ/g
Horizontal Distance = 70Cosα*2*70Sinα/g & 70Cosβ*2*70Sinβ/g
= 1000CosαSinα & 1000CosβSinβ = 480
=> CosαSinα = CosβSinβ = 0.48
=> Sin2α = Sin2β = 0.96
=> 2α & 2β = 73.74 & 106.26
=> α & β = 36.87° & 53.13°
Sinα = 0.6 & Sinβ = 0.8
or Same can be solved
{Sin²α + Cos²α = 1 SinαCosα = 0.48
(Sinα + Cosα)² - 2SinαCosα = 1 => (Sinα + Cosα)² = 1.96
=> Sinα + Cosα = 1.4
(Sinα - Cosα)² +2SinαCosα = 1 => (Sinα - Cosα)² = 0.04
=> Sinα - Cosα = 0.2
Adding Both Sinα = 0.8 Cosα = 0.6 }
=> The bisector of the angle between their directions of projection makes 45° with horizontal
Ratio of their times of flight = Sinα/Sinβ = 0.6/0.8 = 3/4 => 3:4
Max height using V² -U² = 2aS => Height = (70Sinα)²/2*9.8 & (70Sinβ)²/2*9.8
=> S = 90 & 160 Ratio = 9:16
Minimum Speed will be when Vertical Velocity = 0
Only Horizontal Velocity Exists
=> 70Cosα & 70Cosβ => 56 & 42 => 4 : 3
Ratio of their minimum speeds during flights is 4:3
Step-by-step explanation:
The bisector of the angle between their directions of projection makes 45° with horizontal
Ratio of their times of flight = Sinα/Sinβ = 0.6/0.8 = 3/4 => 3:4
Max height using V² -U² = 2aS => Height = (70Sinα)²/2*9.8 & (70Sinβ)²/2*9.8
=> S = 90 & 160 Ratio = 9:16
Minimum Speed will be when Vertical Velocity = 0
Only Horizontal Velocity Exists
=> 70Cosα & 70Cosβ => 56 & 42 => 4 : 3
Ratio of their minimum speeds during flights is 4:3
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