Projectile Motion (in a vaccum)

[RogerDodgr]

issue resolved; thanks dick

Given are listed in photo:
t_f=time final (at impact)
y_max = max height
v_o = initial velocity
final height = initial height = 0
x_f =D = final distance

I am having a problem with this because I know max height time must be half of final time at impact (zero height):
http://www.sudokupuzzles.net/blstc.gif

 

[Dick]

You lost a cos(alpha) around the middle of the page. v0^2=16*D/(cos(alpha)^2*tan(alpha)). Note the squared on the cos(alpha).

 

[Moetasim]

Hello, thank you for your question. Projectile motion in a vacuum is a well-studied and understood concept in physics. It describes the motion of an object that is launched into the air and moves under the influence of gravity alone. In this scenario, there is no air resistance to affect the motion of the object.

From the information provided, it seems that you are trying to solve for the final time at impact (t_f), maximum height (y_max), initial velocity (v_o), final distance (x_f), and initial and final heights (0). It is important to note that in a vacuum, the acceleration due to gravity is constant and equal to 9.8 m/s^2. Using this information, we can use the equations of motion to solve for these variables.

To find the final time at impact, we can use the equation t_f = (2y_max/g)^0.5, where g is the acceleration due to gravity. This equation relates the time of flight to the maximum height reached by the object.

To find the maximum height, we can use the equation y_max = (v_o^2sin^2θ)/(2g), where θ is the angle of launch. This equation takes into account the initial velocity and angle of launch to determine the maximum height reached by the object.

To find the initial velocity, we can use the equation v_o = (x_f/gt_f)^0.5. This equation takes into account the distance traveled and time of flight to determine the initial velocity of the object.

Finally, to find the final distance (D), we can use the equation x_f = v_ot_fcosθ. This equation takes into account the initial velocity, time of flight, and angle of launch to determine the final distance traveled by the object.

I hope this resolves your issue and helps you better understand projectile motion in a vacuum. If you have any further questions, please do not hesitate to ask. Thank you.