You are standing on top of a building that is 75-m high and you throw a 4-kg stone horizontally at a speed of 6.6-m/s. How far from the base of the building will the stone land? (the ground is flat)
To find how far the stone will land from the base of the building, we need to use the equations of motion. In this case, we can use the equation for horizontal motion:
distance = horizontal velocity × time
Since the stone is thrown horizontally, its initial vertical velocity is 0 m/s. The gravitational acceleration acts only in the vertical direction and does not affect the horizontal motion. Therefore, the horizontal velocity remains constant throughout the motion.
Given:
Initial vertical velocity (Vy) = 0 m/s
Horizontal velocity (Vx) = 6.6 m/s
Height of the building (h) = 75 m
Mass of the stone (m) = 4 kg
First, let's find the time it takes for the stone to travel from the top of the building to the ground. We can use the equation for vertical motion:
h = (1/2) × g × t^2
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
By substituting the values, we can find t:
75 m = (1/2) × 9.8 m/s^2 × t^2
t^2 = 75 m / ((1/2) × 9.8 m/s^2)
t^2 = 15.3 s^2
t ≈ √(15.3 s^2)
t ≈ 3.91 s
Now that we know the time it takes for the stone to fall, we can calculate the distance it travels horizontally:
distance = Vx × t
distance = 6.6 m/s × 3.91 s
distance ≈ 25.77 m
Therefore, the stone will land approximately 25.77 meters from the base of the building.