Q1.Invitialy of projectile “ (30î+40î)m/sec
Then find it angle of projection, flight time,
height
and horizontal range (g=10 m/second ²
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Step-by-step explanation:
Given :
Horizontal component of velocity = Vₓ = u cos Ф = 30 m/s
Vertical component of velocity = Vᵧ = u sin Ф = 40 m/s
Acceleration due to gravity = g = 10 m/s²
Solution :
(1) Angle of projection (Ф )
⇒ tan Ф = Vᵧ / Vₓ
⇒ tan Ф = 40/30
⇒ tan Ф = 4 / 3
⇒ Ф= 53°
(2) Time of flight (T)
⇒ T = 2 u sin Ф /g
⇒ T = 2 x Vᵧ / g
⇒ T = 2 x 40 / 10
⇒ T = 8 s
(3) Maximum height (H)
⇒ H = u² sin ² Ф / 2g
⇒ H = u sin Ф x u sin Ф / 2 g
⇒ H = Vᵧ x Vᵧ / 2 x g
⇒ H = 40 x 40 / 2 x 10
⇒ H = 40 x 2
⇒ H = 80 m
(4) Horizontal range (R)
⇒ R = u² sin 2Ф / g
we know that ,
sin 2Ф = sinФ. cosФ
Hence ,
⇒ R = u² sinФ . cos Ф / g
⇒ R = u sin Ф . u cos Ф / g
⇒ R = Vᵧ . Vₓ / g
⇒ R = 40 x 30 / 10
⇒ R = 120 m
Answers :
- The angle of projection is 53 °
- The time of flight of the projectile is8 s.
- The maximum height of the projectile is 80 m .
- The horizontal range of the projectile is 120 m .
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