Answer:
v₀ = 39.2 m/s
Explanation:
Since the air resistance can be negligible, this object is in free-fall. Therefore, we can assume the acceleration is constant and is g = 9.8 m/s².
We know it takes the object 8 seconds throughout the entire flight, but since it is in free fall, we know that it took 4 seconds to reach the top of its trajectory, where the velocity is 0 m/s.
Now we have 3 known variables: time, final velocity, and acceleration. We can solve for initial velocity using this kinematic equation:
- v = v₀ + at
- where v = final velocity, v₀ = initial velocity, a = acceleration, t = time
Substitute known variables into the equation. Assume the positive direction is upwards and the negative direction is downwards.
- 0 = v₀ + (-9.8)(4)
- 0 = v₀ - 39.2
- -v₀ = -39.2
- v₀ = 39.2
The initial velocity of the body is 39.2 m/s.
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You can also solve this question using the displacement of the body. Since it says the body returns to its original position, the displacement is 0 m. Now, you can use the total time, displacement, and acceleration (g) to solve for the initial velocity.
This equation relates all four of these variables:
Substitute all known variables into the equation.
- 0 = v₀(8) + 1/2(-9.8)(8)²
- -8v₀ = -4.9(64)
- -8v₀ = -313.6
- v₀ = 39.2
The initial velocity is the same as we got before: 39.2 m/s.
So, depending on your preference, you can choose which equation to use. Either way, you'll get the same value for the initial velocity.
