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Two bodies are thrown at angles and $θ$ and $(90 - θ)$ from the same point with same velocity 40ms^-1. If the difference between their maximum heights is 20m, the respective maximum heights are (g=10ms^-2)

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25m and 40m

50m and 30m

40m and 25m

40m and 40m

answer is B.

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Detailed Solution

$h_{1} = \frac{40^{2} \sin^{2} θ}{20}$

$h_{2} = \frac{40^{2} \sin^{2} (90 - θ)}{20} = \frac{40^{2} \cos^{2} θ}{20}$

$h_{1} + h_{2} = \frac{40^{2}}{20} = 80$

$h_{1} - h_{2} = 20$

$2 h_{1} = 100$

$h_{1} = 50 m & h_{2} = 30 m$

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