A man stands on the roof of a 19.0 m tall building and throws a rock with a velocity of magnitude 30.0 m/s at an angle of 30.0 degrees above the horizontal. Ignore air resistance. Calculate the horizontal distance from the base of the building to the point where the rock strikes the ground.
To calculate the horizontal distance from the base of the building to the point where the rock strikes the ground, we can use the horizontal and vertical components of the velocity.
The vertical component of the velocity can be found using the equation v_y = v * sin(θ), where v is the magnitude of the velocity (30.0 m/s) and θ is the angle (30.0 degrees).
v_y = 30.0 m/s * sin(30.0 degrees)
v_y = 15.0 m/s
Next, we can use the kinematic equation to find the time it takes for the rock to reach the ground. We'll use the equation d_y = v_iy * t + (1/2) * a * t^2, where d_y is the vertical displacement (19.0 m), v_iy is the initial vertical component of the velocity (15.0 m/s), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time we want to solve for.
19.0 m = (15.0 m/s) * t + (1/2) * (-9.8 m/s^2) * t^2
To solve this quadratic equation, we can set it equal to zero and use the quadratic formula. The equation becomes:
-4.9 * t^2 + 15.0 * t - 19.0 = 0
Using the quadratic formula, t can be solved as follows:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -4.9, b = 15.0, and c = -19.0.
After solving for t, we'll have the time it takes for the rock to reach the ground. Finally, we can calculate the horizontal distance using the equation d_x = v_x * t, where v_x is the horizontal component of the velocity, which can be found using v_x = v * cos(θ).
v_x = 30.0 m/s * cos(30.0 degrees)
v_x = 25.98 m/s
d_x = 25.98 m/s * t
To calculate t using the quadratic formula and then substitute it into the equation for d_x, we can now solve for the horizontal distance.
105 meters
find seconds to reach maximum height which is 1.53 s. Then find time it takes for object to drop 30.5 meters, 2.49 seconds. Add them together then multiply by initial x velocity and you get 105 meters.