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?

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