A marble is dropped from the top of the empire state building.
a. Determine the position and velocity functions for the marble
b. What is the average velocity for the first 3 seconds of flight?
c. Whatisthespeedofthemarblewhent=0? t=3? t=6?
d. How long does a person looking up from the ground have to evade the marble? e. What is the velocity of the marble hitting the ground?
a = g = -9.81 m/s^2
v = -gt = -9.81 t
h = Hi - (1/2) g t^2 = Hi - 4.9 t^2
b)
h at t = 0 = Hi
h at t = 3 = Hi-4.9 t^2 = Hi - 44.1 m/s
average = (-44.1)/3 = - 14.7 m/s
c) at 0 v = 0
at 3 v = -9.81*3 = -29.4 m/s
at 6 v = -9.81*6 = -58.9 m/s
d) well I am not about to Google Hi
Hi = 4.9 t^2
v = -9.81 t
if you were supposed to use feet instead of meters as your other problem that I just saw, use 32 ft/s^2 for g not 9.81 m/s^2
a. To determine the position and velocity functions for the marble, we can use the equations of motion.
Let's assume that the initial position of the marble is 0 (at the top of the Empire State Building) and the initial velocity is also 0 (assuming it is simply dropped). The acceleration due to gravity, g, is approximately 9.8 m/s^2.
The position function for an object in free fall can be expressed as:
s(t) = 0.5 * g * t^2
The velocity function can be obtained by taking the derivative of the position function:
v(t) = g * t
b. To determine the average velocity for the first 3 seconds of flight, we need to calculate the change in position and divide it by the change in time. Since the object is in free fall, the initial and final positions can be calculated using the position function mentioned above.
Using the position function, we have:
s(3) = 0.5 * g * (3^2)
s(0) = 0.5 * g * (0^2)
The average velocity can be calculated as:
average velocity = (change in position) / (change in time)
average velocity = (s(3) - s(0)) / (3 - 0)
c. To determine the speed of the marble at different time points, we need to calculate the magnitude of the velocity at those time points using the velocity function derived earlier.
To find the speed of the marble at t = 0, t = 3, and t = 6, we can substitute those values into the velocity function v(t) = g * t and calculate the magnitude of the resultant velocities.
d. To determine how long a person looking up from the ground has to evade the marble, we need to find the time at which the marble hits the ground. The time it takes for the marble to hit the ground is determined by setting the position function equal to the height of the Empire State Building (approximately 443 meters) and solving for t.
s(t) = 0.5 * g * t^2
s(t) = 443 meters
Solve the above equation for t to find the time it takes for the marble to hit the ground.
e. Finally, to find the velocity of the marble hitting the ground, we can substitute the time obtained in the previous step into the velocity function v(t) = g * t and calculate the velocity of the marble when it hits the ground.
Note: This explanation provides the steps to find the answers to the given questions. You will need to plug in the appropriate values and perform the calculations to get the specific numerical answers.