A projectile is fired from ground level at an angle above the horizontal on an airless planet where g = 10.0 m/s2. The initial x and y components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long after firing does it take before the projectile hits the level ground?

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lublana lublana · Answer 1 · 2020-06-09T05:58:32+02:00

Answer:

10 s

Explanation:

We are given that

[tex]g=10.0m/s^2[/tex]

Initially

[tex]v_x=86.6m/s,y=50.0m/s[/tex]

We have to find the time after firing taken by projectile before it hits the level ground.

v=[tex]\sqrt{v^2_x+v^2_y}[/tex]

[tex]v=\sqrt{(86.6)^2+(50)^2}=99.99 m/s[/tex]

[tex]\theta=tan^{-1}(\frac{v_x}{v_y})[/tex]

[tex]\theta=tan^{-1}(\frac{50}{86.6})=30^{\circ}[/tex]

Now,

[tex]t=\frac{vsin\theta}{g}[/tex]

Using the formula

[tex]t=\frac{99.99sin30}{10}[/tex]

[tex]t=4.99\approx 5 s[/tex]

Now, total time,T=2t=[tex]2\times 5=10s[/tex]

Hence, after firing it takes 10 s before the projectile hits the level ground.