Answer:
a. -39.2 m/s; -78.4 m
b. -31.2 m/s; -46.4 m
c. -47.2 m/s; -110.4 m
Explanation:
<h2>Part (a)</h2>
We are given/can infer these variables:
- t = 4.0 s
- a = -9.8 m/s²
- v_0 = 0 m/s
We want to find the displacement and the final velocity of the rock.
We can use this equation to find the final velocity:
Plug in the known variables into this equation.
- v = 0 + (-9.8)(4.0)
- v = -9.8 * 4.0
- v = -39.2 m/s
The final velocity of the rock is -39.2 m/s.
Now we can use this equation to find the displacement of the rock:
Plug in the known variables into this equation.
- Δx = 0 * 4.0 + 1/2(-9.8)(4.0)²
- Δx = 1/2(-9.8)(4.0)²
- Δx = -4.9 * 16
- Δx = -78.4 m
The displacement of the rock is -78.4 m.
<h2>
Part (b)</h2>
We are given/can infer these variables:
- v_0 = 8.0 m/s
- a = -9.8 m/s²
- t = 4.0 s
We can use this equation to find the final velocity:
Plug in the known variables into this equation.
- v = 8.0 + (-9.8)(4.0)
- v = 8.0 + -39.2
- v = -31.2 m/s
The final velocity of the rock is -31.2 m/s.
We can use this equation to find the displacement:
Plug in known variables:
- Δx = 8.0(4.0) + 1/2(-9.8)(4.0)²
- Δx = 32 - 4.9(16)
- Δx = -46.4 m
The displacement of the rock is -46.4 m.
<h2>Part (c)</h2>
We are given/can infer these variables:
- v_0 = -8.0 m/s
- a = -9.8 m/s²
- t = 4.0 s
We can use this equation to find the final velocity:
Plug in the known variables into this equation.
- v = -8.0 + (-9.8)(4.0)
- v = -8.0 - 39.2
- v = -47.2 m/s
The final velocity of the rock is -47.2 m/s.
We can use this equation to find the displacement:
Plug in known variables:
- Δx = -8.0(4.0) + 1/2(-9.8)(4.0)²
- Δx = -32 - 4.9(16)
- Δx = -110.4 m
The displacement of the rock is -110.4 m.
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