Projectile motion flight time of ball

[ronny45]

[SOLVED] Projectile motion

Homework Statement

A ball is thrown with an intial velocity of v0 at an angle theta from the horizontal. Find the flight time of the ball in terms of H and g only.

Homework Equations

t = (2 v0 sin theta)/g

The Attempt at a Solution

Ok. I found theta to be the tan inverse of 4R/H. Thus, the initial velocity is sqrt[Rg/sin(2tan-1(4R/H))] - a little longwinded but accurate. However, my problem arises when I plug these values into the above equation and those really nasty 'R's refuse to go away, and the problem specifically states that g and H should be my only variables. I feel like i must be missing something really obvious, and if so, i apologise in advance, but please help anyway! Thank you!

 

[rl.bhat]

When the ball reaches the height H, its velocity is equal to zero. So using kinametics equation we get (vosin theta)^2 = 2gH. From this equation find the value of (v0sin theta) and plug it the relevant equation.

 

[ogb p]

Based on the given information, it seems that the problem is asking for the flight time of a projectile, which can be calculated using the equation t = (2v0 sin theta)/g. However, there seems to be some confusion with the variables used in the equation. It is important to note that the variable R represents the horizontal distance from the point of projection to the point where the ball lands, while H represents the vertical distance from the point of projection to the point where the ball lands. Therefore, the values for R and H should be determined based on the given information and then substituted into the equation. Additionally, it is important to ensure that the units for all variables are consistent (e.g. if R is given in meters, H should also be in meters). I would suggest reviewing the problem and double checking the values used for R and H before plugging them into the equation.