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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=AxBx2, 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=102

hence horizontal distance is x=102t

and vertical distance iss=ut+12at2=102t12gt2

therefore h=102t5t2=A×102tB×200t2

102A=102

A=1

200B=5

B=140

therefore A:B=1140=40:1

Alternatively, y=x(ABx)=0 when particle reaches the ground.

Hence, R=AB

But, R=u2×sin(2θ)g=202sin90010=40

AB=40:1


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