Question

From the top of a tower $19.6m$ high, a ball is thrown horizontally. If the line joining the point of projection to the point where it hits the ground makes an angle of $45$ with the horizontal, then the initial velocity of the ball is:

• A. $9.8m{s}^{-1}$
• B. $4.9m{s}^{-1}$
• C. $14.7m{s}^{-1}$
• D. $2.8m{s}^{-1}$

Answer 1

The correct option is A $9.8m{s}^{-1}$

As the angle is 45 the range and height is going to be equal

vertical motion

$S_y=ut+0.5a{t}^2$

$19.6=0+0.5g{t}^2$

horizontal motion

$S_x=ut$

solving above two equations

$S_y=0.5g\times \frac{S_x^2}{u^2}$

$S_x=S_y$

$u^2=0.5g\times 19.6=\frac{1}{2}\times 9.8\times 19.6={9.8}^2$

$u=9.8m/s$