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.
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
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