if a person jumps from the tenth flor 30m to a pool thatis 5m away from the building, with what initial horizontally velocity must the person jump
To determine the initial horizontal velocity required for a person to jump from the tenth floor and reach a pool that is 5m away from the building, we can use the principles of projectile motion.
The horizontal motion of the person jumping will be unaffected by gravity because there is no force acting horizontally. Therefore, the horizontal velocity remains constant throughout the motion.
In this scenario, we can use the equation for horizontal motion:
Distance (d) = Velocity (v) × Time (t)
Since we know the distance the person needs to cover horizontally (5m) and we want to find the initial horizontal velocity (v), let's rearrange the equation:
v = d / t
Now, we need to find the time it takes for the person to fall from the tenth floor and reach the pool. For this, we can use the equation for vertical motion:
Distance (d) = Initial Velocity (u) × Time (t) + 0.5 × Acceleration (a) × Time² (t²)
In this case, the initial vertical velocity (u) is 0 because the person starts from rest, the distance (d) is the vertical distance from the tenth floor to the pool (30m), and the acceleration due to gravity (a) is approximately 9.8 m/s². Rearranging the equation, we get:
d = 0.5 × a × t²
t² = (2 × d) / a
t = √((2 × d) / a)
Now, we can substitute the values into the equation to find the time:
t = √((2 × 30) / 9.8) ≈ 2.19 seconds
Finally, we can use the time obtained to calculate the initial horizontal velocity:
v = d / t
v = 5 / 2.19 ≈ 2.28 m/s
Therefore, for the person to jump from the tenth floor and reach the pool 5m away, they would need an initial horizontal velocity of approximately 2.28 m/s.