Question

an object is dropped from some height for 2.0 s, at which point it is still 60 m above the ground. what will be the velocity of the object when it hits the ground?
if your answer is not an integer, write it to 3 significant figures in standard decimal form.
______ m/s

Explanation:

Step1: Find distance fallen in 2.0 s

Use free-fall displacement formula:
$$\Delta y_1 = \frac{1}{2}gt^2$$
Substitute $g=9.81\ \text{m/s}^2$, $t=2.0\ \text{s}$:
$$\Delta y_1 = \frac{1}{2} \times 9.81 \times (2.0)^2 = 19.62\ \text{m}$$

Step2: Calculate total initial height

Add fallen distance to remaining height:
$$y_0 = \Delta y_1 + 60 = 19.62 + 60 = 79.62\ \text{m}$$

Step3: Find final velocity at ground

Use kinematic formula $v^2 = v_0^2 + 2gy_0$ (initial velocity $v_0=0$):
$$v = \sqrt{2gy_0}$$
Substitute values:
$$v = \sqrt{2 \times 9.81 \times 79.62}$$
$$v = \sqrt{1563.5604} \approx 39.54\ \text{m/s}$$

Answer:

39.5 m/s