a tennis ball is hit vertically upwards with a velocity of 20m/s. what is it's Decelaration as it moves upward? calculate the maximum height reached by the ball.
-9.81 m/s^2
0 = 20 - 9.81 t
then
h = 20 t - 4.9 t^2
or
(1/2) m v^2 = m g h
so
h = v^2/2g
To find the deceleration of the tennis ball as it moves upward, we can assume that the only force acting on it is the force of gravity.
Gravity acts downward and causes the ball to decelerate as it moves upwards. Therefore, the deceleration of the ball is equal to the acceleration due to gravity, which is approximately -9.8 m/s^2 (negative because it is in the opposite direction to the motion of the ball).
Next, to calculate the maximum height reached by the ball, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (which is 0 m/s at the highest point)
u = initial velocity (given as 20 m/s)
a = acceleration (which is -9.8 m/s^2)
s = displacement (maximum height reached)
Rearranging the equation, we have:
s = (v^2 - u^2) / (2a)
Plugging in the values, we get:
s = (0^2 - 20^2) / (2 * -9.8)
s = (-400) / (-19.6)
s ≈ 20.41 meters
Therefore, the maximum height reached by the ball is approximately 20.41 meters.
To find the deceleration of the tennis ball as it moves upward, we need to understand the motion of the ball.
When the ball is thrown vertically upward, it experiences deceleration due to the force of gravity pulling it downward. The acceleration due to gravity is approximately 9.8 m/s² and acts in the opposite direction to the upward motion of the ball.
Therefore, the deceleration of the ball as it moves upward is equal to the acceleration due to gravity, which is -9.8 m/s² (negative because it opposes the upward motion).
Next, let's calculate the maximum height reached by the ball.
We can use the kinematic equation for vertical motion:
vf² = vi² + 2ad
Where:
vf = final velocity (when the ball reaches the maximum height, its velocity becomes zero)
vi = initial velocity (20 m/s, as given)
a = acceleration (deceleration due to gravity, -9.8 m/s²)
d = displacement (maximum height, what we want to find)
Rearranging the equation, we get:
d = (vf² - vi²) / (2a)
Since the final velocity when the ball reaches the maximum height is zero, the equation simplifies to:
d = vi² / (2a)
Substituting the values:
d = (20 m/s)² / (2 * -9.8 m/s²)
Simplifying the equation:
d = 400 m²/s² / (-19.6 m/s²)
d ≈ -20.4 meters
The negative sign indicates that the displacement is in the opposite direction to the motion. In this case, it means the maximum height reached by the ball is 20.4 meters above the launch point.