A ball thrown vertically upward from the ground with an initial velocity of 50m/s. what is the total time spent by the ball in the air
Well, well, just like my dreams of becoming a professional clown seem to fly away, so does this ball! Let's calculate its time in the air, shall we?
When a ball is thrown vertically upwards, it follows a parabolic trajectory. At the highest point, its velocity becomes zero before it starts its descent again. Now, let's consider the upward and downward motions separately.
First, let's find the time it takes for the ball to reach its maximum height:
Using the formula: v = u + at, where v is final velocity, u is initial velocity, a is acceleration, and t is time.
At the highest point, the ball's final velocity is 0, and acceleration due to gravity is -9.8 m/s² (since gravity pulls it downwards).
So, we have the equation: 0 = 50 - 9.8t. Now, solve this equation for time "t."
But wait, there's more! Once it reaches its maximum height, it starts descending. The time taken to reach the maximum height is the same as the time taken to descend, due to the symmetrical nature of the trajectory. Since the ascent and descent take the same amount of time, we can just double the time we found earlier.
So, get your clown calculator out and solve that equation! Once you find the time, double it, and you'll have the total time that the ball spends in the air.
To find the total time spent by the ball in the air, we need to consider the upward motion and the downward motion separately.
First, let's calculate the time taken for the ball to reach its highest point (the maximum height). In this case, the initial velocity (u) is 50 m/s, and the final velocity (v) at the highest point is 0 m/s (as the ball momentarily comes to a stop). We can use the kinematic equation to find the time taken (t):
v = u + at
Since the ball is moving against the gravitational force, the acceleration (a) is -9.8 m/s² (negative since it acts in the opposite direction to the motion).
0 = 50 - 9.8t
Simplifying the equation:
9.8t = 50
t = 50 / 9.8
t ≈ 5.1 s
Therefore, it takes approximately 5.1 seconds for the ball to reach its highest point.
Next, we find the total time spent by the ball in the air by considering the upward and downward motions. The time taken for the upward motion is the same as the time taken for the downward motion (since the magnitudes of the velocities are the same at corresponding heights).
So, the total time spent by the ball in the air can be calculated as twice the time taken to reach the maximum height:
Total time = 2 * 5.1 s
Total time ≈ 10.2 s
Hence, the ball spends approximately 10.2 seconds in the air.
To determine the total time the ball is in the air, we first need to find the time taken for the ball to reach its highest point (at the top of its trajectory) and then double that value.
To find the time taken to reach the highest point, we can use the equation of motion:
v = u + at
Where:
v = final velocity (0 m/s at the highest point)
u = initial velocity (50 m/s)
a = acceleration (due to gravity, approximately -9.8 m/s^2)
t = time taken to reach the highest point
Rearranging the equation to solve for t:
t = (v - u) / a
t = (0 - 50) / (-9.8)
t = 5.1 seconds (approx.)
Since the time taken to reach the highest point is 5.1 seconds, the total time the ball spends in the air can be calculated by doubling this value:
Total time = 2 * 5.1
Total time = 10.2 seconds
Therefore, the ball spends a total time of 10.2 seconds in the air.
time up = time down
total flight time ... 2 * [(50 m/s) / g]