A ball is thrown directly upward at 19.6 m/s how much time passes before the ball reaches the top of its motion
We know that at the top of the motion the velocity of the ball is 0.
Therefore 0 = v + at
0 = 19.6 + (-9.8)t
t = 19.6/9.8
Well, let me calculate that for you.
Did you know that when a ball is thrown directly upward, it's like saying "Hey, gravity, catch!" and the ball goes up and up until gravity has had enough and says "Okay, I'll take it from here" and brings the ball back down? Fun fact!
Anyway, let's calculate the time it takes for the ball to reach the top.
Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration (in this case, gravity, which is approximately -9.8 m/s²) and t is the time taken, we can rearrange the equation to solve for t.
Since the ball reaches the top of its motion, the final velocity (v) is 0 m/s and the initial velocity (u) is 19.6 m/s (upward).
0 = 19.6 + (-9.8)t
Once we solve this equation, we'll find out the time it takes for the ball to reach the top of its motion.
Calculating...
*taps foot*
*time passes*
*still calculating...*
Ah! Here it is!
The time it takes for the ball to reach the top of its motion is approximately 2 seconds.
So, it takes around 2 seconds for the ball to reach the top before gravity goes "catch!" and brings it back down! Fun, right?
To find the time it takes for a ball to reach the top of its motion, we can use the following steps:
Step 1: Identify the given information.
The given information in this problem is the initial velocity (v₀) of the ball, which is 19.6 m/s.
Step 2: Determine the known equation related to the question.
The equation we can use to solve this problem is the kinematic equation for vertical motion:
v = v₀ + at
where:
v is the final velocity (0 m/s at the top),
v₀ is the initial velocity (19.6 m/s),
a is the acceleration (-9.8 m/s²) due to gravity,
and t is the time.
Step 3: Set up the equation and solve for time.
Since the final velocity at the top is 0 m/s, we have:
0 = 19.6 - 9.8t
To solve for t, we can rearrange the equation as follows:
9.8t = 19.6
t = 19.6 / 9.8
Step 4: Calculate the time.
Evaluating the above expression, we find:
t = 2 seconds
Therefore, it takes 2 seconds for the ball to reach the top of its motion.
To find the time it takes for the ball to reach the top of its motion, we can use the kinematic equation:
v = u + at
Where:
v = final velocity (0 m/s at the top)
u = initial velocity (19.6 m/s)
a = acceleration (due to gravity, -9.8 m/s^2)
We need to rearrange the equation to solve for time (t):
t = (v - u) / a
Substituting the values into the equation:
t = (0 - 19.6) / -9.8
Simplifying:
t = -19.6 / -9.8
t = 2 seconds
Therefore, it takes 2 seconds for the ball to reach the top of its motion.