Answer:
Velocity = 4.33[m/s]
Explanation:
The total energy or mechanical energy is the sum of the potential energy plus the kinetic energy, as it is known the velocity and the height, we can determine the total energy.
![E_{M}=E_{p} + E_{k} \\E_{p} = potential energy [J]\\E_{k} = kinetic energy [J]\\where:\\E_{p} =m*g*h\\E_{p} = 4*9.81*0.5=19.62[J]\\E_{k}=\frac{1}{2} *m*v^{2} \\E_{k}=\frac{1}{2} *4*(3)^{2} \\E_{k}=18[J]\\Therefore\\E_{M} =18+19.62\\E_{M}=37.62[J]](https://tex.z-dn.net/?f=E_%7BM%7D%3DE_%7Bp%7D%20%20%2B%20E_%7Bk%7D%20%5C%5CE_%7Bp%7D%20%3D%20potential%20energy%20%5BJ%5D%5C%5CE_%7Bk%7D%20%3D%20kinetic%20energy%20%5BJ%5D%5C%5Cwhere%3A%5C%5CE_%7Bp%7D%20%3Dm%2Ag%2Ah%5C%5CE_%7Bp%7D%20%3D%204%2A9.81%2A0.5%3D19.62%5BJ%5D%5C%5CE_%7Bk%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%2Am%2Av%5E%7B2%7D%20%20%5C%5CE_%7Bk%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%2A4%2A%283%29%5E%7B2%7D%20%5C%5CE_%7Bk%7D%3D18%5BJ%5D%5C%5CTherefore%5C%5CE_%7BM%7D%20%3D18%2B19.62%5C%5CE_%7BM%7D%3D37.62%5BJ%5D)
All this energy will become kinetic energy and we can find the velocity.
![37.62=\frac{1}{2} *m*v^{2} \\v=\sqrt{\frac{37.62*2}{4} } \\v=4.33[m/s]](https://tex.z-dn.net/?f=37.62%3D%5Cfrac%7B1%7D%7B2%7D%20%2Am%2Av%5E%7B2%7D%20%5C%5Cv%3D%5Csqrt%7B%5Cfrac%7B37.62%2A2%7D%7B4%7D%20%7D%20%5C%5Cv%3D4.33%5Bm%2Fs%5D)
Answer:
2.572 m/s²
Explanation:
Convert the given initial velocity and final velocity rates to m/s:
- 65 km/h → 18.0556 m/s
- 35 km/h → 9.72222 m/s
The motorboat's displacement is 45 m during this time.
We are trying to find the acceleration of the boat.
We have the variables v₀, v, a, and Δx. Find the constant acceleration equation that contains all four of these variables.
Substitute the known values into the equation.
- (9.72222)² = (18.0556)² + 2a(45)
- 94.52156173 = 326.0046914 + 90a
- -231.4831296 = 90a
- a = -2.572
The magnitude of the boat's acceleration is |-2.572| = 2.572 m/s².
The formation of a cell plate is a characteristic of cytokinesis in terrestrial plants.
Answer:
6.0 m below the top of the cliff
Explanation:
We can find the velocity at which the ball dropped from the cliff reaches the ground by using the SUVAT equation

where
u = 0 (it starts from rest)
g = 9.8 m/s^2 (acceleration of gravity, we assume downward as positive direction)
h = 24 m is the distance covered
Solving for h,

So the ball thrown upward is launched with this initial velocity:
u = 21.7 m/s
From now on, we take instead upward as positive direction.
The vertical position of the ball dropped from the cliff at time t is

While the vertical position of the ball thrown upward is

The two balls meet when

So the two balls meet after 1.11 s, when the position of the ball dropped from the cliff is

So the distance below the top of the cliff is

Acceleration = (change in speed) / (time for the change.
change in speed = (ending speed) - (starting speed) = 9 m/s.
Acceleration = (9 m/s) / (period of 1) .
We don't know the units of the 'period of 1'.
If it means '1 second', then the acceleration is 9 m/s² .