Solving Kinematics: A Ball Thrown Upward

[therest]

Homework Statement

A ball is thrown vertically upward with a speed of 25.2 m/s.
a)How high does it rise? Answer in units of m.
b) How long does it take to reach its highest point? Answer in units of s.
c) How long does it take the ball to hit the ground after it reaches its highest point? Answer in units of s.
d) What is its velocity when it returns to the level from which it started? Answer in units
of m/s.

Homework Equations

all kinematics equations.
I used x=x0 + v0t + (1/2)at^2, I remember.

The Attempt at a Solution

I have a thru c - a was 32.37, and b abd c were both 2.57 (parabola was symmetrical) but I have no idea how to solve d, at all.

 

[ryan88]

Since the ball is taking the same time to rise as it is to fall again, this would mean that by the time the ball reached the same level it was as at when it started, it would be going the same speed as it was when it was first thrown upwards.

 

[tomcue]

As a scientist, it is important to understand the concepts and principles behind solving problems rather than just relying on memorized equations. In this case, the kinematics equations can be used to solve for the velocity of the ball when it returns to the level from which it started.

We know that the initial velocity of the ball, v0, is 25.2 m/s. At the highest point, the velocity is 0 m/s as the ball momentarily stops before falling back down. Using the kinematics equation v = v0 + at, we can solve for the acceleration (a) of the ball.

0 = 25.2 m/s + a(2.57 s)
a = -9.8 m/s^2

Now that we know the acceleration, we can use the same equation to solve for the velocity (v) at any given time (t). In this case, we are interested in the velocity when the ball returns to the starting level, so we can set x = 0 and solve for t.

0 = 25.2 m/s + (-9.8 m/s^2)t
t = 2.57 s

Therefore, the velocity when the ball returns to the starting level is 25.2 m/s. This makes sense because the ball will have the same velocity as it did when it was thrown upward.

It is important to understand the concepts and principles behind solving kinematics problems rather than just relying on memorized equations. This will allow you to solve a wider range of problems and have a deeper understanding of the concepts.