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a body is projected with a velocity of 40m/s After 2 sec it crosses a vertical pole of height 20.4m Find the angle of projection and horizontal range of projectile

a body is projected with a velocity of 40m/s After 2 sec it crosses a vertical pole of height 20.4m Find the angle of projection and horizontal range of projectile
 

Grade:10

1 Answers

Arun
25750 Points
6 years ago
U = 40 m/s.     The height becomes 20.4 m after 2 sec.

h = u sinФ t - 1/2 g t²
20.4 = 40 sinФ * 2 - 1/2 * 9.8 * 2²
=>  sinФ = 1/10   => Ф = sin⁻¹ 0.10
=>  CosФ = √99 /10     
=> sinФ ≈ 1/10
Hence sin2Ф = 2 sinФ cosФ = 2√99/100
 = √99/50 = 9.949/50 = 0.19898 = 0.2

Horizontal range = u² sin2Ф / g   ≈ 40² * 0.2/9.8 
   R = 32.49 m

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