Question

A baby has a tantrum and throws itself down on the bed that is a distance of .3m below. She hits the bed in 1.5 seconds. What is the initial velocity?

Answer 1

Answer on Question#52859 - Physics - Mechanics - Kinematics - Dynamics

A baby has a tantrum and throws itself down on the bed that is a distance of .3m below. She hits the bed in 1.5 seconds. What is the initial velocity?

Solution:

The dependence of the child’s height above the bed is given by

$$h(t) = h_0 + v_0 t - \frac{g \cdot t^2}{2},$$

where $h_0 = 0.3 \, \text{m}$ – is the initial height, $v_0$ – is the initial velocity, $g = 9.8 \frac{\text{m}}{\text{s}^2}$ – acceleration due to gravity, $t$ – time. Since $h(1.5 \, \text{s}) = 0$, we get the equation for $v_0$:

$$0 = 0.3 \, \text{m} + v_0 \cdot 1.5 \, \text{s} - \frac{9.8 \frac{\text{m}}{\text{s}^2} \cdot (1.5 \, \text{s})^2}{2}$$

Therefore,

$$v_0 = 7.15 \frac{\text{m}}{\text{s}}$$

Answer: $7.15 \frac{\text{m}}{\text{s}}$ (directed upward).

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