Question

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 4.4 ss for the dart to land back at the barrel.What is the maximum horizontal range of your gun (in meters)?

Answer 1

47.48 m

Step-by-step explanation:

The horizontal range of an object can be estimated using the equation below:

`S_(x) =`
`(v^(2)*sin (2\alpha))/(g)`

For the maximum horizontal range to occur, the angle
`\alpha` is 45°. Then, the horizontal range will be:

`S_(x)` =
`(v^(2)*sin 90)/(g) = (v^(2))/(g)`

In addition, the velocity (v) can be estimated using the equation below:

v = gt/2

Therefore, the maximum horizontal range is:

`S_(x) = ((gt/2)^(2))/(g)` = (9.81*4.4/2)^2 / 9.81 = 47.48 m