A ball is thrown horizontally off the top of a 65 m tall building at a velocity of 7.8 m/s. How far did the ball land from the base of the building? Round your answer to 2 decimal places.
To find the horizontal distance the ball travels before it lands from the base of the building, you need to think about the horizontal motion of the ball. Since the ball is thrown horizontally, it does not have any initial vertical velocity. The only force acting on the ball horizontally is the force due to gravity, which remains constant throughout the motion.
To solve this problem, you can use the equation:
Distance = Velocity × Time
1. First, determine the time it takes for the ball to land. To do this, we need to find the time it takes for the ball to fall from the top of the building to the ground. The vertical motion of the ball can be analyzed using the equation:
h = (1/2) * g * t^2
where:
h = height of the building (65 m)
g = acceleration due to gravity (9.8 m/s^2)
t = time taken to fall
Rearrange the equation to solve for time:
t^2 = 2h/g
t = √(2h/g)
Substituting the given values:
t = √(2 * 65 / 9.8)
2. Calculate the time:
t = √13.26
t ≈ 3.64 seconds (rounded to two decimal places)
3. Now, use the time calculated to find the horizontal distance traveled by the ball:
Distance = Velocity × Time
Distance = 7.8 m/s × 3.64 s
Distance ≈ 28.39 meters (rounded to two decimal places)
Therefore, the ball lands approximately 28.39 meters from the base of the building.