A 4.1 kg penguin runs onto a huge sheet of frictionless Antarctic ice. At t=0 it is at x=0 and y=0 with an initial velocity of 0.57 m/s along the positive x-axis. It slides while being pushed by the wind with a force of 0.31 N directed along the positive y-axis. Calculate the magnitude of the penguin's velocity at t = 9.68 s.
(in m/s)
i would explain it to you but it will take a long time. i will be back in 20 min then do it
hang tight
The x-component of the velocity, Vx (0.57 m/s) will not change with time.
The y-component:
Use F=ma to calculate the acceleration in the y-direction. (F=0.31 N, m=4.1 kg)
Initial velocity, v0=0
velocity Vy(t) as a function of time in seconds
Vy(t) = v0.t + (1/2)at²
Combine vectorially the velocities Vx and Vy(t) to get the velocity at any moment in time t.
thanks
You're welcome.
To calculate the magnitude of the penguin's velocity at t = 9.68 s, we will need to consider the forces acting on the penguin and use Newton's laws of motion.
First, let's identify the forces acting on the penguin:
1. The force of the wind pushing the penguin along the y-axis with a force of 0.31 N.
2. The weight of the penguin acting vertically downward, given by W = mg, where m is the mass of the penguin (4.1 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
3. There is no friction or other external forces acting on the penguin in this case.
Next, we need to calculate the acceleration of the penguin using Newton's second law of motion. The net force acting on the penguin is equal to the mass of the penguin multiplied by its acceleration. Mathematically, we can write this as:
ΣF = ma
In this case, the only force acting on the penguin in the y-axis is the force of the wind, so we can write:
F_wind = ma
Plugging in the given values, we have:
0.31 N = (4.1 kg) * a
Solving for acceleration, we find:
a = 0.31 N / (4.1 kg)
Now that we have the acceleration of the penguin, we can calculate the displacement in the y-axis after 9.68 seconds using the equation:
y = y_0 + v_0 * t + (1/2) * a * t^2
Since the initial velocity of the penguin in the y-axis is 0, we can simplify the equation to:
y = (1/2) * a * t^2
Plugging in the given values and solving for the displacement in the y-axis, we find:
y = (1/2) * (0.31 N / (4.1 kg)) * (9.68 s)^2
Next, we can calculate the displacement in the x-axis using the equation:
x = v_0 * t
Plugging in the given values, we have:
x = (0.57 m/s) * (9.68 s)
Now, we can calculate the magnitude of the penguin's velocity at t = 9.68 s using the Pythagorean theorem:
v = √(x^2 + y^2)
Plugging in the calculated values, we find:
v = √((0.57 m/s * 9.68 s)^2 + ((1/2) * (0.31 N / (4.1 kg)) * (9.68 s)^2)^2)
Finally, we can calculate the magnitude of the penguin's velocity at t = 9.68 s by evaluating the expression:
v = √(0.57 m/s)^2 + ((1/2) * (0.31 N / (4.1 kg)) * (9.68 s)^2)^2)
Solve this expression using a calculator to get the answer in m/s.