(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A ball is thrown at angle [itex]\Theta[/itex] and another ball is thrown at an angle (90-[itex]\Theta[/itex]) with the horizontal from the same point with velocity 39.2 m/s. The second ball reaches 50 m higher than the first. Find the heights.

2. Relevant equations

v = u -gt where v is the final velocity and u the initial velocity ( u = 39.2 m/s and v = 0)

S = ut - 1/2 gt^{2}

3. The attempt at a solution

Since the angles were not given, I did not find the vertical and horizontal component of velocity. I tried to find the time taken to reach the maximum height using v = u - gt and got the value as 4. I then substituted this value in the second equation and got the answer as 78.4 m. Since it says that one ball reached 50 m higher, I should either add or subtract 50 from this. Can I assume that this height is of the second ball ? Why not the first ? Even assuming that this is for the second ball, I get the answer as 28.4 and 78.4 m whereas the answer is 14.2 and 64.2.

I then attempted to solve the problem using the second equation by assuming the heights as S and S+50 with u remaining the same. However t would vary and the equation was not leading anywhere.

Where did I go wrong?

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# Heights of two balls thrown at the same time

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