Question

an arrow is thrown in air its time of flight is 5s &the range is 200m Determine the vertical component of the velocity of projection,horizontal component,max.height and angle made with the horizontal.

Answer 1

An arrow is thrown in air its time of flight is 5s; the range is 200m. Determine the vertical component of the velocity of projection, horizontal component, max height and angle made with the horizontal.

Solution:

Let:

$t = 5s$

$S = 200m$

$v_{x}$ — ? horizontal component of velocity

$v_{y}$ — ? vertical component of velocity

$H$ — ? max. height

$\alpha$ — ? angle with the horizontal

The time to rise and the time to slope are equal: $\frac{1}{2} t$

$$H = \frac{1}{2} g \left(\frac{1}{2} t\right)^2 = \frac{1}{2} 9.8 \left(\frac{1}{2} * 5\right)^2 = 30.625\,m$$ $$S = v_{x} * t \Rightarrow v_{x} = \frac{S}{t}$$ $$v_{x} = \frac{200}{5} = 40\,m/s$$ $$H = v_{y} * \frac{1}{2} t \Rightarrow v_{y} = \frac{2H}{t}$$ $$v_{y} = \frac{2*30.625}{5} = 12.25\,m/s$$ $$\alpha = \arctg \left(\frac{v_{y}}{v_{x}}\right) = \arctg \left(\frac{12.25}{40}\right) = 17{}^\circ$$

Answer: $H = 30.625\,m, v_{x} = 40\,m/s, v_{y} = 12.25\,m/s, \alpha = 17{}^\circ$