physics projectile motion and uniform circular motion
 

Ok I had a test today with these questions on it, and I'm completly lost

A projectile reaches its maximum height two seconds after launch. At its max height its speed is 10 m/s.

How far does the particle travel?
What are the x and y components?
How high does it go?

Is it safe to say that the particle travels 40 m because of conservation of energy, because I figured 10 m/s was the initial velocity too?
Is the x component 10i and y component 0j?
I did v^2-vo^2/2a and figured it reached 5.1 m, is this correct?


A particle is in uniform circular motion about the origin of an x-y coordinate system moving clockwise with a period of 7 seconds. At one instant its position vector is 2i-3j

Find speed and magnitude of the acceleration.

I completely dont understand this one!

1) Don't confuse speed with velocity.

2) Is this a calculus-based physics course or algebra-based?

Here are some of my thoughts:

At t=2, the y-component of speed will be zero. The x-component of speed does NOT change during the course of the flight. You can figure out the y-component using the acceleration due to gravity of two seconds (2 seconds to reach the top, two seconds to fall gives you two seconds of the y-component of speed).

For the height and distance (range) problems, you are going to need the angle at which the projectile was shot. Without the angle, you cannot solve the problem.

You are correct it is 40 meters, but for the wrong reason, for a 2d projectile problem, you need to break it up into x and y component.

Since when the projectile is at its peak, there is not velocity in the x direction, we know that the velocity in the y direction is 10 m/s. since we know that it traveled up for 2 seconds, it will travel down for 2 seconds as well, giving us 4 seconds of time in the air, moving in the x direction at 10 m/s giving us 40 meters.

Now we need to find the y component: we know that after 2 seconds it is at its peak

Y = ½ g*t^2 +Vyo*t +Yo.

Yo = 0, initial y position is 0
Vyo = ?, the initial y velocity

Solve for Vyo; 19.6 m/s

So we have Vyo = 19.6 m/s and Vxo as 10 m/s
So since it travels up for 2 seconds we can again use the Y function to solve for the max height now that we have the Vyo.
Vyo = 19.6 meters high.

I’m off to pick up dinner, I’ll try to answer b when I am eating.

Find the length of the position vector, this is the radius. You are given the period.

Now find the circumfrence of the circle. You now have the distance the particle is travelling over a certain amount of time. So you have the speed.

As for the centripetal acceleration it is given by a=(v^2)/r

This is not true. All the information you need to solve the problem is given...

You can determine the maximum height because you know that the y component reaches the maximum height in 2 seconds. This is the equivalent of finding the distance an object travels after accelerating at 1G for 2 seconds...

You can determine the distance of the projectile because you know the time of flight, 2 + 2 = 4 seconds, and you know it's x component velocity, 10 m/s. This works out to 40m.

As you can see, the angle was not needed, here...

PS. I'm sorry I got to this thread so late. This forum is too slow to check too often...