Projectile Motion Tutorial Learning Goal To understand how to apply the equation

Question

Projectile Motion Tutorial Learning Goal To understand how to apply the equations for one-dimensional motion to the x and y directions separately in order to derive standard formulas for the range and height of a projectile A projectile is fired from ground level at time t 0, at an angle with respect to the horizontal. It has an initial speed uo. In this problem we are assuming that the ground is level Part A Find the time tH it takes the projectile to reach its maximum height H Express t H in terms of uo, , and g (the magnitude of the acceleration due to gravity). Submit Hints My Answers Give Up Review Part Incorrect; Try Again; 5 attempts remaining Part B Find tR, the time at which the projectile hits the ground after having traveled through a horizontal distance R Express the time in terms of vo, , and g. sin 2

Explanation / Answer

Projectile

let the initial velocity of projectile is v0 , making angle theta with horizontal , can reach a maximum height H,
and reaches the ground at R distance from point of projection (range).

the horizontal component of velocity vx = v0 cos theta,
vertical component of velocity vy = v0 sin theta.

Time of ascent is time taken by projectile to reach maximum height .

Part A

   Ta = v0 sin /g s

Part B
   t_R is total time taken by projectile when it hits the ground after having traveled t
hrough a horizontal distance R is equal to sum of time of ascent and time of descent

  
   T_R = v0 sin /g + v0 sin /g = 2 v0 sin /g s

PArt C

   maximum height attained by the projectile is

       H max = v0^2 sin^2 /2g m

Part D

   Total horizontal distance travelled is range R = v0^2 sin 2/g m

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