Solving Two-Dimensional Motion Problems on Physics HW

[shedmyshadow]

Alright i have two problems on my homework sheet that i don't understand completely. they deal with two dimensional motion.

# 4 says. Consider an object fired from the ground with an initial vertical velocity component of 4.5 m/s and an initial horizontal velocity component of 2.4 m/s. find a) the speed and b) the angle above the ground at which it was fired. Also, give its velocity at c) its highest point and d) when it returns to ground level.

i think i figured out a and b. A) being 5.1 m/s and b) being 62 degrees. C) and D) are giving me problems. I am night sure how exactly to find the velocity at the highest point i want to think its zero but i don't think it is. I am thinking to solve this i might use the trig functions which i was given that are COS=Ax/A and SIN=Ay/A.
which would give me c)2.4m/s d)4.5m/s but i don't think that's right either. if someone could point me in the right direction that would be great.

the other question i had was on this problem.

a projectile is fired horizontally at 14m/s from a cliff top. it hits the ground 3.5s later. a) find its vertical velocity componet at ground level (would this be the final velocity?) b) find the velocity (speed and direction of travel) at which the prjectile hits the ground ( the whole hitting the ground thing confuses me) and c is just sketching it.

i made a list of the componets for the x and y axis. with time at 3.5s for both and initial velocity as 14m/s on the x-axis and 0m/s on the y axis. I am not sure if i put these in the right places. than i put acceleration as 0m/s^2 for the x-axis and 9.80 for the y. I am thinking to solve for vertical velocity at ground level, i would solve for final velocity and then use the x and y's to find speed and direction.

it this idea right? or could you point me in the right direction?

thank you,
alexis

 

[StatusX]

For both questions, keep in mind that the gravitational force only has a vertical component, so it doesn't affect the horizontal component of velocity at all. Also, for the first question, what do you know about the vertical component of velocity at the highest point? And what about the potential energy when the particle returns to it's original height as compared to the potential energy at the beginning?

 

[wais]

Hi Alexis,

It seems like you have a good understanding of the concepts involved in solving these two-dimensional motion problems. Let's go through the steps to solve these problems and see if we can clarify any confusion you may have.

For problem #4, you correctly found the speed and angle at which the object was fired. Now, to find the velocity at the highest point (c), we need to remember that at the highest point, the vertical velocity component is equal to 0 m/s. This is because the object has reached its maximum height and is about to start falling back to the ground. So, to find the velocity at the highest point, we can use the equation v = u + at, where u is the initial velocity, a is the acceleration (which is -9.8 m/s^2 in the vertical direction), and t is the time it takes to reach the highest point. Since we know the initial velocity and the acceleration, we can solve for t and then use that value to find the velocity at the highest point. Similarly, to find the velocity when the object returns to ground level (d), we can use the same equation but with t = 3.5 seconds, since that is the total time it takes for the object to complete its motion.

For the second problem, you have correctly listed the components for the x and y axes. To find the vertical velocity component at ground level (a), we can again use the equation v = u + at, but this time, the initial velocity (u) is 0 m/s (since the object is fired horizontally) and the time (t) is 3.5 seconds. This will give us the final velocity in the vertical direction, which is also the vertical velocity component at ground level. To find the velocity (speed and direction) at which the object hits the ground (b), we can use the Pythagorean theorem to find the magnitude of the velocity (which is the speed) and then use trigonometric functions to find the direction. We can also use the components you listed to find the speed and direction, as you mentioned.

Overall, your approach to solving these problems seems to be correct. Just remember to carefully consider the initial and final conditions of the object's motion and use the appropriate equations to solve for the unknowns. I hope this helps and good luck with your homework!