PART A:
-9.8 m/s^2 (S)
PART B:
0 meters (N)
PART C:
≈ 7.7 (ROUNDED)
Accurate: 7.69300
PART D:
4.9 m (Δy)
Transcribed Text:
A tennis player tosses a tennis ball straight up and then catches it after 1.57 seconds at the same height as the point of release.
Required:
- Acceleration of the ball while in flight
- Velocity of the ball at maximum height
- Initial velocity
- Maximum height reached
Use the following kinematic equations:
[tex]v=v_o+at[/tex]
Final velocity = Initial Velocity + Acceleration × Time
Δ[tex]x=v_ot+\frac{1}{2}at^2[/tex]
Change in position (displacement) = Initial velocity × time + (0.5) (acceleration × final time)²
[tex]v^2=v_o2+2a[/tex]Δ[tex]x[/tex]
Final velocity (squared) = Initial velocity (two times) + (two times) acceleration * change in position
*A illustration shall be provided for better understanding*
Part A:
Once the tennis player releases the ball, the only force acting on that ball is the gravitational force which exerts an acceleration of -9.8 m/s^2.
Part B:
At that maximum height (as seen in the attached picture) would have a velocity of 0 for just a split moment making this the answer.
PART C: *Be aware that the PART A and B are just conceptual type questions and now we have actual calculations to figure out*.
Reviewing what we know,
Acceleration = -9.8 m/s^2
Time = 2.00 seconds
Now we have to find the initial velocity.
Reviewing the picture and the final velocity, it should turn out this way:
Looking at the kinematic equations we would use:
[tex]V_f=V_i+at[/tex]
Current equation:
[tex]-V_o=V_o+(-9.8)(1.57)[/tex]
* MULTIPLY -9.8 and 1.57!!!
Now we must subtract the V(naught) from both sides.
The left and right side would become:
[tex]-2v_o=-15.38600[/tex]
Divide -2 from both sides.
Initial velocity = 7.69300
Rounded
≈ 7.7 m/s
This would make the initial velocity equal to 7.7 m/s
PART D:
In order to solve for maximum height, we must use some values we would need to find this answer.
Initial velocity = 7.69300 m/s
Acceleration = -9.8m/s^2
Final velocity (or velocity at max height) = 0 m/s
Δy = ...
The kinematic equation we would be using is:
[tex]v^2=v_o2+2a[/tex]Δ[tex]x[/tex]
Because the situation is in the vertical dimension, the 'delta x' will be changed to:
[tex]v^2=v_o2+2a[/tex]Δ[tex]y[/tex]
Subtract the initial velocity squared from both sides of the equation.
This would give us:
[tex]v^2-v_0^2=2a[/tex]Δ[tex]y[/tex]
Divide both sides by 2a.
By finding this we can find the vertical displacement.
[tex]\frac{v^2-u^2}{2a}[/tex]=Δ[tex]y[/tex]
Let plug in the known values
[tex]\frac{(0)^2-(9.8)^2}{2(-9.8^2)} = 4.9m[/tex]
Done