Question

Three balls are kicked from the ground level at some angles above horizontal with different initial speeds. All three balls reached in their paths the samemaximum height. Ball A covered the total horizontal range D; ball B covered the total horizontal range 1.5D and ball C covered total horizontal range 2D when they hit the ground. Which of these three balls spent the greatest time in flight? (section 4.3)

Answer 1

Answer:

They all hit at the same time

Explanation:

Let the time of flight is T.

The maximum height is H and the horizontal range is R.

The formula for the time of flight is

$T=\frac{2uSin\theta }{g}$ ..... (1)

Te formula for the maximum height is

$H=\frac{u^{2}Sin^{2}\theta }{2g}$    .... (2)

From equation (1) and (2), we get

$\frac{T^{2}}{H}=\frac{\frac{4u^{2}Sin^{2}\theta }{g^{2}}}{\frac{u^{2}Sin^{2}\theta }{2g}}$    

$\frac{T^{2}}{H}=\frac{8}{g}$

$T=\sqrt{\frac{8H}{g}}$

here, we observe that the time of flight depends on the maximum height and according to the question, the maximum height for all the three balls is same so the time of flight of all the three balls is also same.