Question

A tourist stands at the top of the Grand Canyon, holding a rock, overlooking the valley below. Find the final velocity and displacement of the rock after 4.0 seconds give the three initial conditions listed below:

a. the rock is dropped vertically from rest
b. the rock is tossed vertically upward with 8.0m/s of speed
c. The rock is tossed vertically downward with 8.0 m/s speed

Answer 1

a. -39.2 m/s; -78.4 m

b. -31.2 m/s; -46.4 m

c. -47.2 m/s; -110.4 m

Step-by-step explanation:

Part (a)

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.

• Δx = ?
• v = ?

We can use this equation to find the final velocity:

• v = v_0 + at

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:

• Δx = v_0 t + 1/2at²

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.

Part (b)

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:

• v = v_0 + at

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:

• Δx = v_0 t + 1/2at²

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.

Part (c)

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:

• v = v_0 + at

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:

• Δx = v_0 t + 1/2at²

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.