Answer:
Explanation:
There's an easy way to answer this and then an easier way. I'll do both since I'm not sure what you're doing this for: physics or calculus. Calculus is the easier way, btw.
Going with the physics version first, here's what we know:
a = -9.8 m/s/s
v₀ = 3.75 m/s
t = ??
That's not a whole lot...at least not enough to directly solve the problem. What we have to remember here is that at the max height of a parabolic path, the final velocity is 0. So we can add that to our info:
v = 0 m/s. Use the one-dimensional equation that utilizes all that info and allows us to solve for time:
v = v₀ +at and filling in:
0 = 3.75 + (-9.8)t and
-3.75 = -9.8t so
t = .38 seconds. This is how long it takes to get to its max height. Another thing we need to remember (which is why calculus is so much easier!) is that at the halfway point of a parabolic path (the max height), the object has traveled half the time it takes to make the whole trip. In other words, if .38 is how long it takes to go halfway, then 2(.38) is how long the whole trip takes:
2(.38) = .76 seconds. Now onto the calculus way:
The position function is
The first derivative of this is the velocity function and, knowing that when the velocity is 0, the time is halfway gone, we will find the velocity function and then set it equal to 0 and solve for t:
v(t) = -9.8t + 3.75 and
0 = -9.8t + 3.75 and
-3.75 = -9.8t so
t = ,38 and multiply that by 2 to find the time the whole trip took:
2(.38) = .76 seconds.
The angle theta of the spring is 31 degrees. To solve for this, show the equation which is equal to the 10lb ball. With this, the unknown will be the angle. Then transpose/transfer the terms in order to isolate the variable for the angle. First solve for s, then solve for angle theta. You will come up with s = .5849 ft and angle theta = 31.2629 or 31 degrees. Hope this helps.
Answer:
Top speed is 31.68 m/s
Explanation:
Speed of a body is the distance traveled by the body in unit time.
Speed is generally expressed in meter per second or kilometer per hour.
Here, the cheetah travels a distance of 274 m in 8.65 s.
Therefore, speed of cheetah is the distance traveled by it in one second.
For 8.65 s, distance traveled is 274 m
For 1 s, distance traveled will be 
meters per second. This value is called speed.
So, speed is given as the ratio of the distance traveled to that of the time taken.
∴ Top speed of cheetah is given as:
Here, 
is the top speed of cheetah.
Answer:
What is the average translational kinetic energy of molecules in an ideal gas at 37°C? The average translational energy of a molecule is given by the equipartition theorem as, E = 3kT 2 where k is the Boltzmann constant and T is the absolute temperature.
Explanation:
The average translational energy of a molecule is given by the equipartition theorem as, E = 3kT 2 where k is the Boltzmann constant and T is the absolute temperature.
Given
Initial velocity:
36 ft/s
Initial height:
0 ft
Vertical motion model:
h(t) = -16t^2 + ut + s
v = initial velocity
s = is the height
Procedure
We are going to use the model provided for the vertical motion.
We know that at the maximum height the final velocity is 0.
Then we will use the following expression to calculate the maximum height:
Now for time:
Solving for t,
The total time the kangaroo takes in the air is 2.3s.
