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22 September, 00:47

You buy a plastic dart gun, and being a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 3.8 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?

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  1. 22 September, 01:56
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    The maximum horizontal range of your gun = 35.378 m

    Explanation:

    By shooting the dart straight up, we can use the equations of motion to evaluate the initial velocity of the dart as it comes out from the gun

    u = initial velocity = ?

    v = final velocity at maximum height = 0 m/s

    g = - 9.8 m/s

    t = time taken to reach maximum height = (total time of flight of the dart) / 2 = 3.8/2 = 1.9s

    v = u + gt

    0 = u - (9.8 * 1.9)

    u = 18.62 m/s.

    To shoot a projectile to obtain maximum range, the angle of shot, θ = 45°

    Range of a projectile is given as

    R = [u² sin (2θ) ]/g = [18.62² (sin (2 * 45°)) ]/9.8

    R = 35.378 m
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