Question

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

Answer 1

[AI-generated answer — Explain Bot]

To find the initial horizontal velocity required for the person to jump from the tenth floor and reach the pool 5 meters away from the building, we can use the principle of projectile motion.

The key to solving this problem is to understand that the horizontal motion and vertical motion of the person jumping are independent of each other.

Let's assume that there is no air resistance. In this case, the only force acting on the person during the horizontal motion is their initial velocity.

Here are the steps to find the initial horizontal velocity:

Step 1: Find the time of flight for the vertical motion.
We need to find out how long it takes for the person to fall from the tenth floor to the pool. We can use the equation of motion for vertical motion:

𝑦 = 𝑣₀𝑡 + (1/2)𝑎𝑡²

Where:
𝑦 = vertical displacement = -30m (negative as it's downward)
𝑣₀ = initial vertical velocity = 0 m/s
𝑎 = acceleration due to gravity = -9.8 m/s² (negative as it's downward)
𝑡 = time of flight (what we're trying to find)

Rearranging the equation, we can solve for 𝑡:

-30 = 0 + (1/2)(-9.8)(𝑡²)
-30 = -4.9𝑡²
𝑡² = 30/4.9
𝑡 = √(30/4.9)

Step 2: Calculate the horizontal distance.
The horizontal distance traveled by the person can be calculated using the equation:

𝑑 = 𝑣₀𝑥 × 𝑡

Where:
𝑑 = horizontal distance = 5m
𝑣₀𝑥 = initial horizontal velocity (what we want to find)
𝑡 = time of flight (from step 1)

Rearranging the equation, we can solve for 𝑣₀𝑥:

5 = 𝑣₀𝑥 × √(30/4.9)
𝑣₀𝑥 = 5 / √(30/4.9)

Calculating the value using a calculator or by simplifying the fraction further, we find:

𝑣₀𝑥 ≈ 6.225 m/s

Therefore, the person must jump with an initial horizontal velocity of approximately 6.225 m/s to reach the pool 5 meters away from the building.