Question

3 formula 1 point a worker drops their hard hat while they are up on scaffolding. the hat started at a height of 10.3 meters. assuming that ground level is at a height of 0 meters, what must be the displacement of the hat when it strikes the ground? answer 4 multiple choice 1 point a ball is initially at rest and falls a distance of δy to the ground. the ball has an acceleration of g. which equation below could be used to find the time for the ball to fall to the ground below in terms of the given variables? gt² √(g/2) √(2δy/g) 1/2gt² -g²/2t

Explanation:

3.

Step1: Define displacement

Displacement is the change in position. Initial height $h_i = 10.3$ m and final height $h_f=0$ m.
Displacement $\Delta h=h_f - h_i$

Step2: Calculate displacement

$\Delta h=0 - 10.3=- 10.3$ m. The negative sign indicates the direction is down - ward.

We use the kinematic equation for vertical motion $y - y_0=v_0t+\frac{1}{2}at^{2}$. Since the ball is initially at rest $v_0 = 0$, and the acceleration $a = g$ and the displacement $\Delta y=y - y_0$. So, $\Delta y=0\times t+\frac{1}{2}gt^{2}$. Rearranging for $t$:
First, we have $\Delta y=\frac{1}{2}gt^{2}$. Then $t^{2}=\frac{2\Delta y}{g}$, and $t = \sqrt{\frac{2\Delta y}{g}}$.

Answer:

$-10.3$ m

4.