Question

A ball is shot from the ground into the air. At a height of 10.80 m, the velocity is observed to be v = (8.10 m/s) i + (7.10 m/s) j.
What is the maximum height that the ball will rise?

   What will be the total horizontal distance traveled by the ball?

    What is the x-component of the final velocity of the ball?

What is the y-component of the final velocity of the ball when it lands back on the ground?

Answer 1

Hmax = h + v0y^2/(2*g)

   = 10.8 + 7.1^2/(2*9.8)

   = 13.372 m <<<<<<<<<<<----Answer

time taken to reach same height in air

t1 = 2*voy/g = 2*7.1/9.8 = 1.449 s

let t2 is the time taken to rach ground

y = voy*t + 0.5*g*t^2

10.8 = 7.1*t2 + 4.9*t2^2

4.9*t2^2 + 7.1*t2 - 10.8 = 0

solving the above equation we get

t2 = 1.001 s

so total time taken, t = t1+t2 = 2.45 s

x = Vox*t = 8.1*2.45 = 19.845 m <<<<<<<---answer

vx = vox = 8.1 m/s <<<<<---Answer

vy = -voy - g*t2 = -7.1 - 9.8*1.001 = -16.9 m/s <<<<<<---Answer