Question

questions

1. a ball is dropped from a cliff and hits the ground 3.2 seconds after. how high up was the cliff?
2. a ball is thrown straight up. when the ball reaches the highest point, what is its speed?
3. a man drops a rock from the top of a 22 meter cliff. how long does it take for the rock to hit the ground?
4. a penny is dropped off the empire state building (380m). with what speed does the penny hit the floor?
5. michael jordans vertical leap is reported to be 1.22m. what speed does he leave the ground? we assume ( v_{f} ) is 0
6. an arrow is launched straight up from the ground with an initial velocity of 33.4 m/s. what is the highest point it reaches?
7. a woman throws an egg from the top of a building with an initial speed of +5 m/s. the egg cra the base of the building 12 seconds after it was thrown. what is the final velocity of the egg?

match the answers to the color and number below
#1 - yellow → (-50.23 m) #2 - blue → (0)
#3 - orange → (2.12 s) #4 - green → (-86.35 m/s) #5 - brown → (4.89 m/s)
#6 - red → (-56.86 m) #7- grey → (-112.72 m/s)

Explanation:

Step1: Identify the kinematic equation

The kinematic equation for vertical motion under gravity when the initial velocity \(v_{0} = 0\) is \(x=x_{0}+v_{0}t+\frac{1}{2}at^{2}\). Here, \(x_{0}\) is the initial position (height of the cliff, let \(x_{0}=h\)), \(x = 0\) (ground level), \(v_{0}=0\) (dropped), and \(a=-g=- 9.81m/s^{2}\), \(t = 3.2s\).
Substituting into the equation: \(0=h+0\times t+\frac{1}{2}\times(-9.81)\times t^{2}\)

Step2: Solve for \(h\)

$$
LATEXBLOCK0
$$

Answer:

\(50.23m\) (matches with \(\#1 - Yellow\))