A missle is projected with a velocity of 150m/s at an angle of tita to the vertical if the total time of the flight of the missle is 25 sec. Find the value of tita
To find the value of theta, we need to use the equation for the vertical component of projectile motion:
Vertical displacement (y) = initial vertical velocity (Vy) * time (t) + 0.5 * acceleration due to gravity (g) * time^2
Since the missile was projected with an angle of theta to the vertical, the initial vertical velocity is given by:
Vy = 150m/s * sin(theta)
The vertical displacement can be assumed to be zero, since the missile lands on the ground and returns to the same vertical position:
0 = 150m/s * sin(theta) * t - 0.5 * 9.8m/s^2 * t^2
Simplifying this equation, we get:
0 = 150 * sin(theta) * 25 - 0.5 * 9.8 * 25^2
0 = 150 * sin(theta) * 25 - 1225 * 25
0 = 3750 * sin(theta) - 30625
3750 * sin(theta) = 30625
sin(theta) = 30625 / 3750
sin(theta) = 8.17
However, the value of sin(theta) cannot exceed 1 since it represents the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Therefore, there is no value of theta that satisfies this equation, and the given information is not possible.