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 compo

Question

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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Khang Minh 5 years 2021-09-02T13:41:51+00:00 1 Answers 73 views 0

Answers ( )

  1. Philomena
    0
    2021-09-02T13:43:34+00:00
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    Answer:

    10 s

    Explanation:

    We are given that

    g=10.0m/s^2

    Initially

    v_x=86.6m/s,y=50.0m/s

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

    v=\sqrt{v^2_x+v^2_y}

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

    \theta=tan^{-1}(\frac{v_x}{v_y})

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

    Now,

    t=\frac{vsin\theta}{g}

    Using the formula

    t=\frac{99.99sin30}{10}

    t=4.99\approx 5 s

    Now, total time,T=2t=2\times 5=10s

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

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