A man stands on the roof of a 10.0 -tall building and throws a rock with a velocity of magnitude 30.0 at an angle of 34.0 above the horizontal. You can ignore air resistance.
Calculate the horizontal distance from the base of the building to the point where the rock strikes the ground.
Dimensions must be provided with numbers.
To calculate the horizontal distance from the base of the building to the point where the rock strikes the ground, we can apply the basic principles of projectile motion.
Step 1: Split the initial velocity into horizontal and vertical components.
The horizontal component of the initial velocity (Vx) can be calculated using the equation Vx = V * cos(θ), where V is the magnitude of the initial velocity (30.0 m/s) and θ is the launch angle (34.0°).
Vx = 30.0 * cos(34.0°) = 24.97 m/s
Step 2: Calculate the time of flight.
The total time of flight (T) can be determined by finding the time it takes for the rock to reach its maximum height and then double that time. Since the vertical motion is symmetric, the time taken to reach the maximum height will be half the total time of flight.
The time to reach maximum height (T_max) can be calculated using the equation T_max = Vy / g, where Vy is the initial vertical component velocity and g is the acceleration due to gravity (9.8 m/s²).
Vy = V * sin(θ) = 30.0 * sin(34.0°) = 16.45 m/s
T_max = 16.45 / 9.8 = 1.68 s
Thus, the total time of flight (T) is double the time taken to reach maximum height: T = 2 * T_max = 2 * 1.68 = 3.36 s.
Step 3: Determine the horizontal distance.
The horizontal distance (D) can be calculated using the equation D = Vx * T, where Vx is the horizontal component of the initial velocity and T is the time of flight.
D = 24.97 * 3.36 = 83.87 m
Therefore, the horizontal distance from the base of the building to the point where the rock strikes the ground is approximately 83.87 meters.