First slide

Projection Under uniform Acceleration

Question

Two balls are thrown from the top of a tower of unknown height with same speed 10 m/s. One is projected at an angle $45^{o}$ above the horizontal and other is projected $45^{o}$ below the horizontal. The difference between the ranges of two projectiles is _______

Moderate

A

2 m
B

6 m
C

10 m
D

cannot be determined

Solution

$\begin{array}{l} R_{1} = u_{x} t_{1} \\ R_{2} = u_{x} (t_{1} + T) \\ R_{2} - R_{1} = u_{x} T \\ = u_{X} \frac{2 u_{y}}{y} \end{array}$
$\begin{array}{l} = \frac{u \cos 45^{0} \times 2 u \sin 45^{0}}{g} \\ = \frac{10 \frac{1}{\sqrt{2}} 2 . 10 \frac{1}{\sqrt{2}}}{10} \\ = 10 m \end{array}$

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