Question

An object is projected with a velocity of $20m/s$ making an angle of ${45}^o$ with horizontal. The equation for the trajectory is $h=Ax-{Bx}^2$ where $h$ is height, $x$ is horizontal distance, $A$ and $B$ are constants. The ratio $A:B$ is $(g=10{ms}^{-2})$

• A. $1:5$
• B. $5:1$
• C. $1:40$
• D. $40:1$

Answer 1

The correct option is D $40:1$

Horizontal velocity, $v_x=20cos\left({45}^o\right)=10\sqrt{2}m/s$

Vertical Velocity , $v_y=20sin\left({45}^o\right)=10\sqrt{2}m/s$

Using $s=ut+\frac{1}{2}a{t}^2$ $h=10\sqrt{2}t-\frac{1}{2}\times 10\times t^2$ ....1

$\Rightarrow x=10\sqrt{2}t$ $\Rightarrow t=\frac{x}{10\sqrt{2}}$

Put the value of $t$ in equation 1, we get

$h=x-\frac{1}{40}{x}^2$,

By comparing the given equation of trajectory, $\Rightarrow A=1$ and $B=\frac{1}{40}$

Hence, $A:B=1:\frac{1}{40}=40:1$