If x and y coordinates of a projectile as a function of time (t) are given as 24t and 43.6t-4.9t^2 , respectively, then the angle (in degrees) made by the projectile with horizontal when t=2 s is ______.

Step-by-step solution

The velocity components of the projectile are given by the derivatives of the position coordinates with respect to time. v_x = dx dt = d dt (24t) = 24 v_y = dy dt = d dt (43.6t - 4.9t^2) = 43.6 - 9.8t At t = 2 s, the velocity components are: v_x = 24 v_y = 43.6 - 9.8(2) = 43.6 - 19.6 = 24 The angle made by the velocity vector with the horizontal is given by: = v_y v_x = 24 24 = 1 = 45^ Answer: 45