Question

1. your sibling drops your keys out of a window, as shown in the image. what is the velocity of the keys when you catch them? given: s = 4.3 g = 9.8m/s² v₁ = 0m/s unknown = vf 2. suppose a free - fall ride at an amusement park starts at rest and is in free fall. a. what is the velocity of the ride after 2.3 s? b. how far do people on the ride fall during the 2.3 - s period? 3. a student drops a ball from a window 3.5 m above the sidewalk. how fast is it moving when it hits the sidewalk? given: s = 3.5 g = 9.8m/s² v₁ = 0m/s unknown = vf 4. you decide to flip a coin to determine whether to do your physics or english homework first. the coin is flipped straight up a. what are the velocity and acceleration of the coin at the top of its trajectory? b. if the coin reaches a high point of 0.25m above where you released it, what was its initial speed?

Explanation:

1.

Step1: Identify the kinematic - equation

We use the equation $v_{2}^{2}=v_{1}^{2}+2as$. Here, the initial velocity $v_{1} = 0\ m/s$ (assuming the keys are dropped), the acceleration $a = g=9.8\ m/s^{2}$ and the displacement $s = 4.3\ m$.
$v_{2}^{2}=0 + 2\times9.8\times4.3$

Step2: Calculate $v_{2}$

$v_{2}=\sqrt{2\times9.8\times4.3}=\sqrt{84.28}\approx9.18\ m/s$

Step1: Use the velocity - time kinematic equation

The equation for velocity in free - fall is $v = v_{1}+at$. Since the ride starts from rest, $v_{1}=0\ m/s$, $a = g = 9.8\ m/s^{2}$ and $t = 2.3\ s$.
$v=0+9.8\times2.3$

Step2: Calculate the velocity

$v = 22.54\ m/s$

Step1: Use the displacement - time kinematic equation

The equation for displacement in free - fall is $s=v_{1}t+\frac{1}{2}at^{2}$. Since $v_{1} = 0\ m/s$, $a = g=9.8\ m/s^{2}$ and $t = 2.3\ s$.
$s=0\times t+\frac{1}{2}\times9.8\times(2.3)^{2}$

Step2: Calculate the displacement

$s = 25.921\ m$

Answer:

$9.18\ m/s$

2.a