Final answer:
The body will reach the ground in 1 second and will strike the ground at a horizontal distance of 25 meters from the point of projection.
The correct answer is C.
Step-by-step explanation:
To find the time taken by the body to reach the ground, we need to consider its vertical motion. The vertical motion is governed by the equation:
h = ut + (1/2)gt^2
Where h is the vertical displacement, u is the initial vertical velocity, g is the acceleration due to gravity, and t is the time taken.
Since the body is projected upward at an angle of 30° with the horizontal, its initial vertical velocity can be found using the equation:
u = usin(theta)
Where u is the initial speed and theta is the angle of projection. In this case, the initial speed is given and theta is 30°. Therefore, the initial vertical velocity is:
u = 50.0 m/s * sin(30°) = 25.0 m/s
Using the equation for vertical displacement, we can solve for time:
-20.0 m = (25.0 m/s)t + (1/2)(9.8 m/s^2)t^2
Simplifying the equation, we get a quadratic equation:
4.9t^2 + 25.0t + 20.0 = 0
Solving this equation, we find t = 1 second or t = -4 seconds. Since time cannot be negative, the body will reach the ground in 1 second.
To find the horizontal distance from the point of projection to where it strikes, we can use the equation:
d = ucos(theta)t
Where d is the horizontal distance, u is the initial speed, theta is the angle of projection, and t is the time taken. Substituting the given values, we get:
d = 50.0 m/s * cos(30°) * 1 s = 25 m
Therefore, the body will strike the ground at a horizontal distance of 25 meters from the point of projection.