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 4.6 s for the dart to land back at the barrel.

Answer 1

Answer:

$R_{max} = 51.84 m$

Explanation:

When we shoot the dart upwards the time taken by the dart to go straight up and again come back is given as

$t = 4.6 s$

here we can say

$\Delta y = 0 = v_i t + \frac{1}{2}at^2$

$0 = v_i t - \frac{1}{2}(9.8)t^2$

put t = 4.6 s then we have

$v_i = 22.54 s$

Now in order to find the maximum range we can say

$R = \frac{v^2 sin2\theta}{g}$

so in order to have maximum range we can say

$\theta = 45 degree$

$R_{max} = \frac{v^2}{g}$

$R_{max} = \frac{22.54^2}{9.8}$

$R_{max} = 51.84 m$