Respuesta :
Answer:
a) It takes 7.5 s for the nickel to fall.
b) The speed will be 79.5 m/s
Explanation:
The equations for the height and velocity of the nickel at time "t" are the following:
y = y0 + v0 · t + 1/2 · g · t²
v = v0 + g · t
Where:
y = height of the nickel at time t
y0 = initial height
v0 = initial velocity
t = time
g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive)
v = velocity at time t
a) When the nickel hits the ground its height is 0. Then, using the equation for height, we can calculate the time it takes the nickel to fall.
y = y0 + v0 · t + 1/2 · g · t²
0 = 324 m - 6 m/s · t - 1/2 · 9.8 m/s² · t²
0 = -4.9 m/s² · t² - 6 m/s · t + 324 m
Solving the quadratic equation:
t = 7.5 s
It takes 7.5 s for the nickel to fall.
b) The speed at which the nickel hits the ground will be the speed after 9 s of falling. Then, using the equation of velocity:
v = v0 + g · t
v = -6 m/s - 9.8 m/s² · 7.5 s
v = -79.5 m/s
The speed will be 79.5 m/s
(a) The time is taken by the nickel to fall is 7.5 seconds.
(b)the speed at which the object strikes the ground is known as the striking velocity. The speed at which the nickel strikes the ground is 79.5 m/sec².
What is velocity?
velocity is defined as the rate of change of the displacement or the height attained in a particular direction. it is a time-based quantity.
it is denoted by u for the initial velocity while u for the final velocity. its si unit is m/sec.
The following given data is given,
Height of tower (h) = 324 m
Initial velocity (u)= 6 m/sec
gravitational acceleration (g) = -9.81 m/sec² (-ve shows the direction is downward)
According to the second equation of motion,
[tex]\rm{H = ut + \frac{1}{2}gt^2}[/tex]
[tex]\rm{324 = 6t -\frac{1}{2}\times9.81t^2}[/tex]
[tex]\rm{324 = 6t -4.9t^2}[/tex]
On solving the quadratic equation we get,
t = 7.5 second
Hence the time is taken by the nickel to fall is 7.5 seconds.
From newtons first equation of motion, we get
[tex]\rm{V = u + gt }[/tex]
[tex]\rm{V = 6 - 9.81\times 7.5[/tex]
[tex]\rm{V = 79.5 m/sec}[/tex]
Hence the speed at which the nickel strikes the ground is 79.5 m/sec².
To learn more about the velocity refer to the link;
https://brainly.com/question/862972
