A projectile is fired from the ground at an angle of 30^ with the horizontal. It lands on a raised terrace of height 25 m after a flight time of 5 s. The initial speed of the projectile is (Take g = 10 m/s ^2 )

Step-by-step solution

Let the initial speed be u . The vertical component of the initial velocity is u_y = u 30^ . Using the equation of motion for the vertical direction: y = u_y t - 1 2 gt^2 Substituting the given values ( y = 25 m, t = 5 s, g = 10 m/s ^2 ): 25 = u_y(5) - 1 2 (10)(5)^2 25 = 5u_y - 125 5u_y = 150 u_y = 30 m/s Since u_y = u 30^ : 30 = u 1 2 u = 60 m/s Answer: 60 m/s