    Question

# An object is projected with a velocity of 20m/s making an angle of 45 with horizontal. The equation for the trajectory is h=Ax−Bx2, where h is height, x is horizontal distance, A and B are constants. The ratio A:B is- (g=10m/s2)

A
1:5
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B
5:1
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C
1:40
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D
40:1
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Solution

## The correct option is A 40:1 horizontal and vertical component of velocity are same and equal to 20cos45o=10√2 hence horizontal distance is x=10√2t and vertical distance iss=ut+12at2=10√2t−12gt2 therefore h=10√2t−5t2=A×10√2t−B×200t2 10√2A=10√2 A=1 200B=5 B=140 therefore A:B=1140=40:1Alternatively, y=x(A−Bx)=0 when particle reaches the ground.Hence, R=ABBut, R=u2×sin(2θ)g=202sin90010=40 ⇒AB=40:1  Suggest Corrections  0      Similar questions
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