A hopper jumps straight up to a height of 0.45 m. With what velocity will it return to the table?

3 m/s

Explanation:

We can solve with kinematics or with energy.

Using kinematics, and taking down to be positive, we're given:

Δy = 0.45 m

v₀ = 0 m/s

a = 10 m/s²

Find: v

v² = v₀² + 2aΔy

v² = (0 m/s)² + 2 (10 m/s²) (0.45 m)

v = 3 m/s

Or, we can use energy.

PE = KE

mgh = ½ mv²

v = √(2gh)

v = √(2 × 10 m/s² × 0.45 m)

v = 3 m/s

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see earlier