Question

A dart leaves a toy dart gun with initial velocity of 7.76 m/s, regardless of the angle it is fired. What is the maximum horizontal distance that the dart can travel? Assume that the dart gun is fired at ground level.

Answer 1

`x( \theta) = (v_0^(2) sin(2\theta))/(g) \\ \\ (dx)/(d \theta) = - ( 2v_0^(2) )/(g) cos(2 \theta) = 0 \\ \\ 2 \theta = ( \pi)/(2) \\ \\ \theta = ( \pi)/(4) \\ \\ x_m_a_x = x( ( \pi)/(4) )= (v_0^(2) sin( ( \pi)/(2) ))/(g)`

Answer 2

6.14m

Explanation: No CaP