Question

From the top of the tower 156.8m high a projectile is thrown with a velocity of 39.2 m/s making an angle of 30

Answer 1

equation of motion for the projectile 

y  = x  tanФ  -  g x² Sec² Ф / (2 u²)

=>  y = x/√3   -  9.8 (4/3) x²/ (2 * 39.2²)             as  Ф  = 30°

=> y = x/√3  - x² /235.2

At  t=0,   x =0  and y = 0 

We have to find x when y = - 156.8 m

so:   x²/235.2 - 156.8 - x/√3  = 0

 =>  √3 x²  - 235.2 x - 235.2 * 156.8√3 = 0

  x = [ 235.2 + - √(235.2² + 4 * 235.2 * 156.8 * 3) ] / (2√3)

    = [ 235.2 + - 235.2 *√(1+8) ]/(2 √3)

    =   2 * 235.2 /√3  meters   or   ignoring negative value.

This is the distance from the foot...

Time taken to hit the ground =  x /(u cosФ)

 = [ 2 * 235.2/√3 ] / (39.2 * √3 / 2)  sec

 = 8 sec