Question

Suppose an object with initial acceleration of 10ft/s^2 is dropped from 300 ft. above the earth. How far would it travel in the first 2 seconds of its journey? Assume initial velocity is zero.

Answer 1

Answer on Question #48471 – Math – Calculus

Suppose an object with initial acceleration of $10ft/s^2$ is dropped from 300 ft. above the earth. How far would it travel in the first 2 seconds of its journey? Assume initial velocity is zero.

Solution:

$$\begin{array}{l} a = 10 \frac{ft}{s^2} - \text{initial acceleration} \\ h_1 = 300 ft - \text{initial height}; \\ t = 2s - \text{time of the journey}; \\ v_0 = 0 - \text{initial velocity}; \end{array}$$

Equation of motion for the object:

$$\Delta h = h_2 - h_1 = v_0 t + \frac{(a + g) t^2}{2} = 0 + \frac{(a + g) t^2}{2}$$ $$\Delta h(2 \sec) = \frac{(a - g) t^2}{2} = \frac{\left(10 \frac{ft}{s^2} - 32.17 \frac{ft}{s^2}\right)(2s)^2}{2} = 44.3 ft$$

Answer: object will travel distance 44.3 ft.

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