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Grade: 11
A ball thrown at different angles with the same speed u and from the same point and it has the same range in both cases. If y1 and y2 are the heights attained in two cases, then y1 + y2 is equal to
  1. u^2/g
  2. 2u^2/g
  3. u^2/2g
  4. u^2/4g
3 years ago

Answers : (1)

Raman Mishra
67 Points
Two projectiles have the same range if they are launched at angles which are complementary to each other. That is, if the 1st projectile is launched at an angle \theta from the horizontal, then the other projectile must be launched at an angle of \frac{\pi }{2} -\theta from the horizontal for having the same range.
Now, maximum height of a projectile = h = \frac{u^{2}\sin ^{2}\theta}{2g} 
For the 1st ball we have h_{1} = \frac{u^{2}\sin ^{2}\theta}{2g}
For the 2nd ball, we have h_{2} = \frac{u^{2}\sin ^{2}(\frac{\pi }{2}-\theta )}{2g}= \frac{u^{2}\cos ^{2}\theta }{2g}
       \therefore   h1 + h2 = u2/2g
3 years ago
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